On what grounds would it be right for me to break fellowship with other believers?

This text is from a transcript of a talk by David Gooding, entitled ‘Unity, Origin and Victory’ (1987).

I think here we have to attempt by God's grace to hold the kind of balance that John would hold. When we talk of heretics, we must be aware of what we're talking—we're talking about enemies of God. We must never allow our desire to stand loyal to the Lord and to stand against heretics to topple over into hardness of spirit against true believers. The Old Testament tells us of a man whose name was Jephthah. After fighting some splendid battles for the Lord, he went down to the fords of Jordan and when fellow Israelites came across, he said, 'Say "shibboleth"', and some of them, they meant to say it, but couldn't quite say it the right way round and they said, 'sibboleth', so he cut their heads off. They were his own Israelite brethren, and gave only a slightly different pronunciation that meant the same, but he cut their heads off. He's not surely held out to us an example to follow. You must be able to distinguish between enemies of God and children of God.

That said, we must distinguish: we must go on the other side. Notice what Scripture says: that true love for the children of God will mean that we keep the commandments of God. Now surely there are bigger and lesser things? There are things that are fundamental and there are things that are not fundamental. In the governing of a church, for instance, elders will want to see that church carry out the commandments of God as they understand them. When it comes to the Lord's people, some of us don't always obey holy Scripture as we should. So I presume elders in a church have a right to ask members of the church to obey holy Scripture—at least what this church believes is the commandment of the Lord. And they who hold the different opinion will presumably respect the elder of the church and not ruin the order of a church in order to press something that even they themselves do not regard as a fundamental.

In other words, receiving all who are the Lord's people, as surely we are commanded to. On the other hand, who we allow to teach in the church—that's a different story altogether, and sometimes we confound those two things, don't we? Yes, receive all the Lord's people who are living godly lives; but who you allow to teach is a different story.