Let me commence by saying that the title “the Limits of Fellowship” is misguided. I know I chose it myself, but it is the wrong question. It starts us off looking for the negative when the theme of the Bible is the positive.
In as much as we are able we are to live at peace with all people. We are pray for our enemies, seek their welfare, not answer evil for evil, and never take revenge (Romans 12:14-21). We are to love one another and by quiet honest work not be trouble makers to others but live properly before outsiders (1 Thessalonians 4:9-11).
And when people come to us in the name of our Lord Jesus Christ we are to welcome them. Our welcome is not for the sake of disputes. We are not to be judgemental. Nor are we to exercise our freedom in Christ to harm the weak whose conscience is bound. Rather we are to serve and build one another in love (Romans 14-15).