It is commonly alleged by those in favor of "secularism" that one of its great selling points is that it can bring peace and stability to society, while non-secular societies are going to be rife with conflict and strife. Let's take a look at this idea just a little more closely and see if it holds up in theory.
For our purposes, secularism refers to the idea that civil government should avoid taking sides in worldview/religious disputes. Secularism implies a state that refuses to endorse or reject any particular worldview or set of beliefs that belongs to any worldview. In other words, secularism implies a religiously neutral civil government.
Let's consider the various kinds of societies, in broad outline, that can exist, and see if we have any reason to believe that secularism's claim to be the ultimate producer of peace and stability can withstand scrutiny.
1. First of all, we can imagine what I will call a pluralistic, pietistic, tolerant, non-secular society. What I mean by this is a society full of citizens/residents where there is a large amount of significant worldview-diversity (pluralism) among the citizens/residents, but where the citizens/residents (can I just call them "citizens" for short from now on to save space?) have no real concern to have their own ideals, beliefs, values, or goals reflected in the actions and policies of the governing institutions (pietism). The society is non-secular, and so the civil government does not claim to be neutral but straightforwardly and honestly adopts a disputed set of beliefs and values and bases its laws and policies on them. However, it also displays a great deal of tolerance towards those who do not share the official government worldview.
It would seem that such a society is likely to be very peaceful and stable, at least with regard to disputes that might originate from differing worldviews. Since the citizens in the society are allowed to live their own private lives in accordance with their own beliefs and values due to a policy of broad toleration, while they have no desire to have their views reflected in government policies, there is no recipe here for significant conflict. (Of course, one can raise the question of whether an entire population in the real world is likely to be pietistic to this extent.)
2. Secondly, we can consider a society that is pluralistic, non-pietistic, tolerant, and non-secular. The key difference between this society and the first one is that the citizens are not content merely to live out their private lives in accordance with their own beliefs and values. They also have a strong desire that the civil government follow their own beliefs and values in policy-making and law-making. They hold their values and beliefs to be important not just to themselves but to the general good and the well-being of society, and they want society's policies and laws to be wise and just (as they count wisdom and justice).
This society is going to be prone to conflict and will lack stability. It is full of people who have completely different ideas of the true and the good, all of whom wish their ideas to be reflected in official law and policy. The problem, of course, is that there can only be one set of laws and policies for a unified society, and those laws cannot reflect everyone's conflicting viewpoints. As the state is non-secular, it will have a straightforwardly-acknowledged official worldview guiding its public policy. The citizens whose views coincide with this official public worldview will be likely to be satisfied with this state of affairs, while those whose views are at odds with the reigning paradigm are likely to be dissatisfied with the situation, even if the state tolerates their dissident views in private life. Conflict may be significantly diffused if the state allows some kind of legal processes, however long-term, by which dissidents can work within the system to try to alter the overarching constitutional order and thus the reigning paradigm of the society (such as by allowing amendments to the Constitution to be made by a certain number of votes). However, this will be unlikely to resolve all societal tension. Even with a legal process for change in place and available, it will be difficult in a pluralistic society to get the society to permanently and with stability endorse anyone's particular point of view. As all sides of a particular dispute can use the same legal channels, it will be hard for one group to establish any kind of permanent dominance for its views over other existing views. A pluralistic society of this sort is thus likely to forever be like a see-saw, constantly going back and forth between conflicting views and policies. If the disputed matters are highly important to the parties (think of something like abortion, where both sides feel crucial, fundamental rights are at stake), there will likely be an increasing frustration as the parties realize they will never really be able to make the society what they want it to be so long as it remains non-pietistically pluralistic. This seems likely to eventually lead either to the breaking up of the society or to serious and even violent conflict, assuming the pluralism remains in place.
3. Now let's imagine a society that is pluralistic, pietistic, tolerant, and secular. This society is like the first society except that it is secular--that is, it claims not to have an established official worldview but to be neutral between contested worldview beliefs in the society.
This society, like the first, will likely be prone to peace and stability, for the same reasons as the first society was. If secularism vs. non-secularism has any effect at all, it will likely be towards slightly decreasing the amount of peace and stability. A secular society claims to be neutral between viewpoints and to treat all viewpoints equally. However, it is actually impossible for a state to be neutral in this way (especially in a pluralistic society). Different worldview beliefs lead to different values, and different values lead to different ideas as to what is good, worthwhile, beneficial, etc., both at an individual level and on a societal level. Therefore, a pluralistic society will have differing ideas as to what laws and policies in a society are truly good and wise. The state, in embracing some particular set of values, priorities, goals, policies, etc., will of necessity end up endorsing the ideals of one or some groups of people over others'. Especially in a deeply pluralistic society (like the modern USA), there simply will not be enough items agreed upon between those with differing worldviews to provide a sufficient foundation for governmental law and policy without the government having to add to those items other controverted ideas and ideals. So religious or worldview neutrality is really impossible for a single society. (For more argumentation on this point, see here, here, and here.) Therefore, any promise of neutrality made by a secular civil government will be necessarily deceptive. It will promise a kind of equality to all the citizens and their views that it can't really deliver. The society, as it must go on and make laws and policies in order to survive, will in fact adopt some set of controversial ideas and ideals anyway, all the while claiming it is not doing so. It will encourage citizens who don't share the concealed official viewpoint to think that their views are equally honored in the society when they truly are not. This situation is likely to bring resentment, as citizens with minority worldviews come to expect society to be more congenial to themselves and their values than is really the case. There would be less resentment, and thus less tension, if the society would simply come out and declare honestly and straightforwardly what its official viewpoint is and thus encourage its pietistic minority citizens to remain pietistic and not get their hopes raised too high.
4. Next, we can imagine a society that is pluralistic, non-pietistic, tolerant, and secular. This society is like society #2, except that it is secular.
This society is going to be prone to conflict and instability, for the same reasons as society #2 was. Will the society's being secular help? I don't really see how. In society #2, the civil government adopted a contested point of view as the basis upon which to make law and policy. The conflict arose because the non-pietistic population was not content to let views contrary to their own dominate political policy. The same situation will be in play here, the only difference being that the civil government will be pretending not to have a controversial official worldview while in reality it does. I suppose this might appease a few very stupid people who also don't really care all that much about what is true and good, and it also might make those with a majority viewpoint who don't think too deeply feel better about themselves, as if their views aren't being favored any more than anyone else's (though they really are). But it is more likely to exacerbate the problems had by society #2 for the reasons I mentioned when discussing society #3: A non-secular government might take views at odds with your beliefs and values, but at least it is honest and straightforward about it. A secular society, on the other hand, may just as much hold views contrary to yours, but it will disingenuously try to make you think that it is not doing so, that it is treating your views fully equally with all other views. This is likely to increase rather than decrease tensions among those with minority viewpoints. Also, a non-secular government, because it is fully aware and up-front about its controversial positions, is likely to be more aware than a naive or disingenuous non-secular government will be about the possible desirability of allowing societal tension to be diffused by means of putting in place legal processes towards change that minorities can avail themselves of. A secular government, on the other hand, may be less likely to consider carefully such an idea, since it denies outright that there are any minority views in the society (after all, how can there be views that are out of accord with the official viewpoint of the civil government--which is what I mean by "minority views"--if the civil government is neutral?). Thus, I must conclude that the secularism of this society is likely to make it less rather than more stable and peaceful than the otherwise comparable non-secular society #2.
5. OK, now let's consider a society that is pluralistic, pietistic, non-tolerant, and non-secular.
This society, for obvious reasons, is going to be prone to strife and instability. Even though the citizens are pietistic, yet they still hold beliefs and values that they consider important to their private lives. Insofar as the state refuses to allow them to hold and practice these beliefs and values, there is likely to be conflict. Of course, toleration comes in degrees. We can think of a society that allows dissident beliefs and values to be held and practiced in private life, but not in public view. (Imagine, for example, if Jews were allowed to be Jews and live as Jews in their private lives, but were not allowed to go outside in Jewish dress, erect publicly-visible synagogues, etc.) We can think of a society that goes further than this and outlaws even private beliefs and practice (insofar as such things can be witnessed enough to come to government attention). And we could imagine other forms of non-toleration as well. I think we can say, generally, that the less tolerant a pluralistic society is, the less peaceful and the more unstable it is likely to be, all other things being equal. A pluralistic society is a society full of people with different worldviews, different beliefs and values. If we make the way of life of a large group of people illegal in a society, we are courting serious resistance and thus conflict. For example, some people in Germany and the USA, and probably other western countries, want to outlaw male infant circumcision, including for religious reasons. What baffles me is how they never seem to realize just how impractical that idea is. Jews, and those who would sympathize with Jews if persecuted, make up a significantly large part of the populations of these countries. To ban an essential practice of Judaism (and apparently Islam as well, or so I'm told) would result in mass unrest and chaos.
6. Now, a society that is pluralistic, non-pietistic, non-tolerant, and non-secular.
Need we say much here? Obviously, this society is going to be significantly more unstable and chaotic than society #5.
7. What if we make the society pluralistic, pietistic, non-tolerant, and secular?
It's hard to see how making the society secular is going to have any influence to make the society more stable or peaceful. Again, as we saw earlier, a secular society is one that is disingenuous towards those with minority views, and thus, if anything, is simply going to increase rather than decrease tension. Secularism might even possibly have the effect of encouraging a society towards more non-toleration: A non-secular society knows and acknowledges that it disfavors certain views, and thus it is likely to consider how those holding such views should be treated. On the other hand, a secular society denies that it disfavors anyone's views (while doing so anyway), so it might be less inclined to consciously consider how tolerant its policies are towards dissidents in some cases. It might be less tolerant in some cases without noticing, due to a naivete arising from its secular philosophy. On the other hand, perhaps secularism might be more likely in some ways to be tolerant than a non-secular society, in that a society can only go so far in terms of discriminating against minorities before the illusion of neutrality comes to be in grave danger of bursting.
8. How about pluralistic, non-pietistic, non-tolerant, and secular?
Again, I don't see how secularism would make this society any more stable than society #6.
9. Now, let's imagine some non-pluralistic societies. I'm going to look at these more briefly and in a single point, because once we've gotten rid of pluralism, we've removed the basic cause of worldview conflict, as is evident from what we've seen.
Obviously, a tolerant, pietistic, non-pluralistic society is going to be prone to peace and stability. But a non-tolerant, non-pietistic, non-pluralistic society will also preserve overall peace and stability, because there will only be a very few people in it with minority views. All societies are intolerant towards some ideas and actions of some members of the society. For example, in the modern USA, we are intolerant towards theft and human sacrifice. Are there people in our society who want to steal, think it's OK to steal, and actually steal? Obviously. Are there people in our society who think it is good thing, or even a religious virtue, to practice human sacrifice? I would be surprised if there weren't. However, these ideas and ideals are enough of a minority that those who have and practice them do not make up a significant portion of the population--or, to put it another way, the society is not really significantly pluralistic with regard to these ideas and practices. Therefore, we can be intolerant towards them (by making them illegal) without undermining our overall peace and stability as a society. And this will be the case generally with such uncommon views. In a biblical theocracy, for example, where the public expression of idolatrous worship would be outlawed, so long as the population does not become significantly pluralistic regarding such matters, the outlawing of these things will not tend to decrease peace and stability. More likely, it will increase peace and stability, as it will discourage pluralism in these areas from developing and reinforce publicly-shared values. (Of course, throughout this whole examination, I've been looking at these things from a purely human point of view, not taking into account how God would bless a society favorable to his will and curse a society non-favorable.)
It seems to me it would make little difference whether a non-pluralistic society were secular or non-secular. It would have little practical reason to be secular, as there would be little point in pretending to be neutral.
So let's consider what we've learned through this little exercise. Our goal was to examine more closely the theoretical claim that secularism will tend to make human societies more peaceful and stable. We have not seen any reason at all to think that that is the case. If anything, secularism might, in some circumstances, make a society somewhat less stable and peaceful, but it's hard to see how it would be at all likely to make it more so. I think we can conclude that if it is peace and stability we are after, secularism is a useless dead-end. Getting rid of pluralism, on the other hand, would seem to be a very good move, if it could be done in a peaceful way (such as through large amounts of voluntary conversions to a single worldview ideology).