"Sinful Disunity"

The OPC has a very helpful article on the unity of the church.  Among many other worthwhile comments in its overall discussion of the issue, the article has this to say about denominational divisions in the church:

There exists between us and all other churches a sinful disunity that demands reconciliation in a biblical way.

Why are denominational divisions sinful?  It is because there is one Body of Christ, and the member churches of that body are to exist in formal communion with each other.  True churches of Christ deserve to be treated as true churches of Christ, and that manifests itself by existing in formal unity.

1. All saints, that are united to Jesus Christ their Head by His Spirit and by faith, have fellowship with Him in His graces, sufferings, death, resurrection, and glory: and, being united to one another in love, they have communion in each other's gifts and graces, and are obliged to the performance of such duties, public and private, as do conduce to their mutual good, both in the inward and outward man.

2. Saints by profession are bound to maintain a holy fellowship and communion in the worship of God; and in performing such other spiritual services as tend to their mutual edification; as also in relieving each other in outward things, according to their several abilities, and necessities. Which communion, as God offereth opportunity, is to be extended unto all those who, in every place, call upon the name of the Lord Jesus.  (Westminster Confession of Faith 26, "Of the Communion of Saints") 

When denominations are separated from each other, they are not treating each other as true churches of Christ.  They are not manifesting the fellowship that is necessarily implied in the relationship between true churches.

The visible unity of the Body of Christ, though not altogether destroyed, is greatly obscured by the division of the Christian church into different groups or denominations. In such denominations Christians exercise a fellowship toward each other in doctrine, worship, and order that they do not exercise toward other Christians. (OPC Form of Government, Chapter IV)

It follows from the above that denominational separation between true churches is inherently and always sinful, because it involves true churches treating each other as if they are not true churches, which is a violation of justice, in the same way as it is a violation of justice when spouses do not treat each other as spouses, or when children do not treat their parents as their parents (or vice versa), or when citizens do not treat civil magistrates as civil magistrates (or vice versa).  The only way a church can be justified in remaining separate from other churches is if it has just cause to reject the de jure legitimacy and authority of those churches.  In other words, if there is just cause to refuse to formally acknowledge a particular church as being a true church, only then do other true churches have the right (and the duty) to remain formally separated from it.  Otherwise, such separation is sinful schism of the Body of Christ.

Does your denomination have the right to exist separately from other denominations?  By doing so, it is declaring that all these other denominations lack de jure legitimacy and authority as churches (though not necessarily de facto being as churches).  If your denomination does attribute de jure legitimacy to other denominations, then its separate existence is not justified and, in order to avoid being sinfully schismatic, it must do what it can to end its separate existence immediately and to join and act in full communion with all other de jure denominations.

For more, see here, here, and here.

UPDATE 12/15/14:  Some have said that it is inappropriate for one denomination to label all others separate from it as "schismatic," but this is clearly implied in the OPC's statement that "[t]here exists between us and all other churches a sinful disunity that demands reconciliation in a biblical way."  If the division between the OPC and, say, the PCA involves "sinful disunity," then who is doing the sinning?  Whose act of remaining separate is sinful?  It must be either the OPC or the PCA, or both.  Does the OPC believe that it is acting schismatically in not seeking immediate union with the PCA?  Presumably not.  Does the OPC believe that it has errors in doctrine or practice that make it inappropriate for the PCA and other denominations to join with it?  Presumably not.  Well then, if the OPC believes that the PCA and other denominations can unite with it without sin, and that it is doing right in remaining separate from the PCA and other denominations, it follows that the OPC is accusing the PCA and the other denominations separate from the OPC of being schismatic in maintaining a separation that need not exist or in maintaining errors in doctrine and practice that create a bar to unification.  If the PCA has errors in doctrine or practice that require the OPC to remain separate from her, then the PCA is behaving schismatically in doing so.  If the PCA has no errors in doctrine and practice that require continued separation, then the OPC has a duty to unity with her right away and is behaving schismatically if it does not.  If the OPC tries to unite with the PCA and the PCA refuses, then the PCA is behaving schismatically in continuing to refuse to unite.  Therefore, however we slice it, the OPC, assuming it is acting in accordance with its own professed principles of church unity, in remaining separate from the PCA must be declaring the PCA to be schismatic.