“As for a person who stirs up division, after warning him once and then twice, have nothing more to do with him, knowing that such a person is warped and sinful; he is self-condemned.” (Titus 3.10) {scriptures are from Titus unless otherwise noted}
Titus was stationed in Crete to put the churches in order (1.5). Most of the letter to Titus is concerning how to mold local congregations into thriving families. To thrive, Titus must teach the congregations to leave unprofitable and worthless practices and to promote submission to good works (cx. 3.9; 2.1, 14}.
What does that look like? Titus would need to begin worshipping and spending time with the local brethren. At some point, he would notice and action (or inaction) that is considered “the thing to do”. He would then need to address it with the congregation. The next step would be for the congregation to change its practices. Would everyone agree to change?
Paul does not tell Titus to encourage churches to split because of personal preferences, this is condemned in verse nine. The word “dissentions” [ESV], or “contentions” [KJV] is something Paul wrote to Corinth about as well. In 1 Corinthians 3.3, Paul uses this same word to tell those brethren that their focus is not on Christlikeness, and it is one of the reasons they are not growing. Notice, Paul is not talking about numbers of people in the congregation, but the spiritual maturity. In Galatians 5.20, KJV calls these works of the flesh “variance”. Such “variances” are condemned with every other evil thing. And Timothy is told such brethren are “depraved” (1 Timothy 6.3-5). Scripture is not neutral or silent on church splits.
Titus’s instruction is not to bless those who are leaving the congregations because of preference. “Have nothing more to do” with “warped and sinful” brethren, is very clear language of condemnation. This is for the good of the faithful. The faithful remnant should notice an increase in spiritual maturity beginning to take root. The men would exhibit deeper understanding in teaching scripture, and women would develop and show off their “Proverbs 31” benevolence.