Let's look at another example of a supposed neutral position that is really not neutral at all: the teaching of evolution in public educational institutions. In accordance with our ideal of worldview and religious neutrality, we seek not only to base laws on neutral grounds, but we also attempt to establish neutrality as a foundation in any of the government's operations, including public education. Hence, the First Amendment and the Supreme Court rulings that support the neutrality principle are applied to the public schools as well. In the late 1980's, the state of Louisiana passed an Act that made it illegal to teach the theory of evolution in the public schools without also balancing that teaching with an alternative view known as “creation science.” In 1987, the Supreme Court struck down this Act, declaring it unconstitutional, in the court case Edwards vs. Aguillard. The Act was struck down for a number of reasons, one of which being that the Act seemed to be grounded in the motive of promoting specific religious beliefs and lacked “a clear secular purpose.” The Court declared that “The Act impermissibly endorses religion by advancing the religious belief that a supernatural being created humankind” (http://caselaw.lp.findlaw.com/scripts/getcase.pl?navby=CASE&court=US&vol=482&page=578).
However, this is an illusion. Banning creationism and teaching evolution in the classrooms violates the ideal of neutrality just as much as would banning evolution and teaching creationism. Think about it. Everybody can agree that a class which attempts to explore the subject of the origin and age of the earth and life would want to get the facts straight, right? Nobody would want egregious error taught as fact in the science classroom. It is assumed that when mainstream science and religious texts come into conflict, the objectively rational thing to do is to go with the mainstream scientific account of the evidence over the religious text. But notice that this way of thinking is based on certain worldview assumptions: What should happen when the Bible and scientific explanations of the data conflict? To say that the Bible should give way to science is to make the assumption that the Bible, in fact, is not the infallible Word of God. If the Bible really is the infallible Word of God, it would be absurd to favor the opinions of the mainstream scientific community over the teachings of the Bible.
Imagine that you hold this belief: There is good, conclusive reason to believe that the Bible is the infallible Word of God, and that everything it teaches is certainly true. This is a belief held, for example, by many evangelical Christians. Imagine you saw eye-to-eye with them on this point. Imagine, also, that you hold that the young-earth creationist interpretation of the Book of Genesis is indeed the correct interpretation. Now, let's look again at what we should do when the Bible comes into conflict with mainstream science: If the Bible is the Word of God, then the creation accounts in the Book of Genesis contain eyewitness testimony to the events that took place during the creation of the universe, the earth, and life, and the eyewitness is none other than the actual Creator himself, who is omniscient and omnipotent and is incapable of being in error or of lying. How much weight should we give to an account of creation coming from the infallible Creator himself!? And what if this account is in conflict with the account of the history of the earth and life provided by the mainstream scientific consensus? Well, where did that consensus come from? It came from a bunch of fallible scientists attempting to figure out as best they could over a period of about 150 years or so how the earth and life came about by means of clues like bits of rock, chemical analyses, etc. Moreover, these scientists themselves admit emphatically that they are not perfect and are quite capable of error, and that their theories are not at all certain but could possibly be wrong. Eugenie Scott, for example, of the National Center for Science Education, in her book Evolution vs. Creationism (ABC-CLIO, Incorporated, 2005), discusses the various kinds of ideas held by scientists. She calls “core ideas” those scientific ideas that are the most firmly established by the evidence (this group would include the age of the earth and evolution). She says, "Indeed, we must be prepared to realize that even core ideas may be wrong, and that somewhere, sometime, there may be a set of circumstances that could refute even our most confidently held theory” (p. 9). She says that “The anthropologist Ashley Montagu summarized science rather nicely when he wrote, 'The scientist believes in proof without certainty, the bigot in certainty without proof' (Montagu 1984: 9).” Arthur N. Srahler, in his book Science and Earth History: The Evolution/Creation Controversy (Buffalo, NY: Prometheus Books, 1987), said this: “Let us admit that the human mind or brain will never be privy to truth, but rather agree that the special kind of observation statement that is a scientific statement, despite being put forward as being true, actually contains a certain probability of being in error. . . . There always is the possibility, no matter how small it may be, that a scientific statement is false. . . . I would like to limit the definition of a 'scientific statement' to one that is subject to a finite probability, no matter how small, of being in error when it is asserted to be correct” (p. 7).
So, on the one hand, we have a creation account that we have good, conclusive reason to believe is an eyewitness account of the creation of the universe, earth, and life by the infallible Creator himself. On the other hand, we have the probable conclusions of fallible scientists doing the best they can to figure out what happened from clues while admitting that everything they say just might possibly (but not likely) be wrong. Which account are we going to go with? It seems to me obvious that we would want to go with the Bible over against the mainstream scientific consensus. That is the obvious, reasonable choice, granting our starting assumptions. If the public educational institutions reject the Bible's creation account from being included in science classes and instead teach a scientific theory that is in conflict with it, this clearly reveals an underlying assumption that the Bible is not, in fact, the infallible Word of God (or at least that the young-earth creationist interpretation of it is incorrect). This would be to endorse a set of beliefs held by liberal Christians and agnostics, for example, over against the beliefs held by many evangelical Christians. There is no way to neutrally decide this issue. If we include the Bible and treat it as the infallible Word of God, we are endorsing one set of worldview beliefs over others. If we exclude the Bible and teach contradicting ideas, we are endorsing another set of worldview beliefs over contrary beliefs. If you are tempted to respond to this dilemma by saying something like, “That's ridiculous! Of course teaching evolution and not using the Bible in science classes is neutral! After all, the Bible is a religious text and evolution is based on the facts of science!” then you have not yet gotten my point. To you, it might seem obvious that the truth of the matter is that the Bible's creation story is not a factually reliable basis for understanding what really happened in earth history and that the mainstream scientific account is better supported by all the evidence, but that conclusion of yours is based in certain assumptions about the nature of the Bible that are different from the assumptions involved in other people's worldviews. Perhaps your assumptions about the Bible are right and the assumptions of many evangelical Christians (which are a part of their core worldview) are wrong, and therefore the public educational institutions should endorse your assumptions over theirs. But to assert this, of course, is to abandon the ideal of neutrality and instead to propose that public institutions endorse your worldview beliefs over others because they are right. Whatever we do with regard to teaching evolution, or with regard to the legalization of same-sex marriage, or with regard to a whole host of other things, we must inevitably establish certain worldview beliefs over others as the official beliefs of the society, in contradiction to the ideal of neutrality.
UPDATE: I just came across (on Facebook, from the Facebook page "Science is Awesome") a quotation by Ann Druyan, wife of the late Carl Sagan, commenting on her husband, which provides another example of the common claim that scientific analysis does not provide certain but only probable conclusions:
It takes a fearless, unflinching love and deep humility to accept the universe as it is. The most effective way he knew to accomplish that, the most powerful tool at his disposal, was the scientific method, which over time winnows out deception. It can't give you absolute truth because science is a permanent revolution, always subject to revision, but it can give you successive approximations of reality.
Notice also in this quotation the assumption that the "scientific method" (which is probably here used in contrast with more purely philosophical reasoning) is the best way to find truth. This is another good example of how the Naturalistic worldview (with its often empiricist epistemology) is often assumed in the scientific disciplines, thus biasing them towards a distorted picture of how we can gain information about reality.