I previously posted on the meaning of the “heretic” of Titus 3:10. To complete that post, here is the note from the new NIV Study Bible:
Someone who absolutely will not abide by the Christian message and apostolic doctrine.
nothing to do with.
Probably indicates what was later called excommunication: these people were not welcome at the Lord’s table until they repented and were restored (see 1 Cor 5:11–13 ; 2 Thess 3:14–15 ; 1 Tim 1:20 and notes). Jesus gave instructions for dealing with people who condemn themselves by refusing to come to terms with their transgression ( Matt 18:15–17 ).
Again, the man in question is one who rejects the Gospel and all that comes with it – not someone who merely disagrees with local leaders on what to do about the roof.