When should a church remove someone from fellowship?

A church should remove someone from fellowship only after first dealing with them in meekness, helping them recognize and confess their sin and gain victory over it. If they persistently refuse to repent, then Paul instructs the church to put that wicked person away until they come to their senses.

Les explains that the unsaved world is God's prerogative to judge, never ours (s341-s343). But within the church environment, Paul says to put away from among yourselves that wicked person (s344-s346). This removal comes only after having dealt with them, trying to get them to recognize their sin and confess it and get victory over it (s347-s349). If they refuse and will not, then Paul says put them aside until they come to their senses (s350-s352). The attitude must be one of meekness, not pride, realizing we also could be tempted and fall into the same trap (s316-s324). We are to bear one another's burdens and help them overcome weaknesses, encouraging them that there is no need to live in sin (s327-s335).

1 Corinthians 5:13

But them that are without God judgeth. Therefore put away from among yourselves that wicked person.

When should a church remove someone from the congregation for unrepentant sin?

The church should remove someone only after first dealing with them, trying to get them to recognize their sin, confess it, and gain victory over it. If they refuse and will not repent, Paul says to put them aside until they come to their senses—removing the wicked person from among the congregation.