Three key verses from the passage in 2 Thessalonians 3:6–15 teach us to be “set apart as a local church from all affiliations, fellowship, and cooperation from professing Christians whose practices deny their confession of faith.”
6 Now we command you, brothers, in the name of our Lord Jesus Christ, that you keep away from any brother who is walking in idleness and not in accord with the tradition that you received from us…. 14 If anyone does not obey what we say in this letter, take note of that person, and have nothing to do with him, that he may be ashamed. 15 Do not regard him as an enemy, but warn him as a brother. (ESV)
Some Christians were apparently “walking in idleness” and refusing to “work quietly and… earn their own living,” a way of life instructed by Paul (2 Thess 3:11; cf. 1 Thess 4:11). The church was to “take note of that person, and have nothing to do with him,” with the goal “that he may be ashamed,” repent, and be restored to the fellowship of the church. They were to “warn him as a brother.”
Whatever other doctrine and truth is included in “the tradition that you received from us,” a phrase that Paul uses to refer to all that he taught the Thessalonians and, by extension, all the churches of Christ, if a brother walks out of accord with this tradition, Christians should have nothing to do with him. Again, the goal is to expose the disobedient brother’s sin and bring shame, moving him to repentance. Until such a time, this brother is not an enemy, but he should be warned as a brother.
Implied, I believe, is this—if a group of Christians (e.g., a local church, denomination, or Christian organization) collectively walks in obvious discord with the tradition of truth given to us Scripture, then a local church should separate from this group as a whole. Perhaps this group’s disobedience is to extend Christian fellowship to another group of so-called Christians who deny cardinal doctrines of the Christian faith. Perhaps their disobedience is something else whereby their works deny their profession of knowing God (Titus 1:16). Whatever it is, if the believer or group of believers clearly and intentionally disobeys Scripture, we should withhold our fellowship from such a one or group because of their disobedience.