How should Christians deal with non-committed Christians with little conviction? Is this a sign of an unregenerate heart?
There are many assumptions and some tensions in your question! Perhaps I can restate it. It might help us to see the issues more clearly! ‘If a professing Christian is not particularly committed in faith and in life, in doctrine and in practice, does this indicate that they are not genuinely converted?’
We must take account of the fact that hypocrites – both deliberate deceivers and the self-deceived – can be robustly orthodox and thoroughly active, if with the wrong foundations and motivations. However, our Lord does make clear that, generally speaking, false teachers (and those who follow them) will be known by their fruits: ‘Do men gather grapes from thornbushes or figs from thistles? Even so, every good tree bears good fruit, but a bad tree bears bad fruit. A good tree cannot bear bad fruit, nor can a bad tree bear good fruit. Every tree that does not bear good fruit is cut down and thrown into the fire. Therefore by their fruits you will know them’ (Matthew 7:16-20).
