"WARN A DIVISIVE PERSON ONCE, and then warn him a second time. After that, have nothing to do with him" (Titus 3:10). It is worth reflecting a little on what this does and does not mean, and how it fits into broader streams of biblical theology.
First, the passage is written to a church leader responsible for maintaining church discipline. It does not sanction a personal vendetta: Christian X decides that Christian Y is rather divisive and therefore decides to have nothing further to do with Y. (Indeed, that itself would exemplify a divisive spirit!) This is written to a Christian who has responsibility for leading and disciplining the church.
Second, the passage focuses on discipline at the local level; it is not introducing infinitely broad approval of all ecumenical thrusts---a kind of condemnation of anyone who does not approve the latest inter-church project or confession. Of course, there may be implications for the broader work of the Gospel, but we must above all grasp what force the text has in its own context.
Third, the immediate evidence of a divisive spirit, in this context, is an unrepentant argumentativeness about peripherals: Christians must "avoid foolish controversies and genealogies and arguments and quarrels about the law, because these are unprofitable and useless" (Titus 3:9). Undoubtedly there is some common understanding between Paul and Titus on these matters that is a little difficult to probe. Paul is certainly not saying, for instance, that every question about the Law is a waste of time; he himself elsewhere discusses the subject. But controversies calculated to divide Christians without producing any gospel strength or moral improvement are "unprofitable and useless." One begins to suspect that those who are stirring up such strife have invested so much of their own egos in their eccentric positions that they can neither be corrected nor back down.
Fourth, if "have nothing to do with him" entails excommunication from the local church (as I think it does), we should reflect on the categories of sin that call forth this sanction in the New Testament. One is major doctrinal aberration, especially among teachers; a second is major moral defection, such as the case described in 1 Corinthians 5; and the third is here---a loveless, untransformed stance that refuses to see the centrality and glory of the Gospel but proves so divisive, despite repeated warnings, that the only solution is to cut the canker from the body. These three categories are the inverse of the patterns of life set out as the three primary tests of genuine Christianity in 1 John: doctrinal probity, moral conformity, and love for the brothers and sisters.