We are called to examine ourselves to see whether we are really Christians. Not every who calls Jesus Lord is a Christian. Not even everyone who thinks they are a Christian is one. That is one very important thing to remember.
Another thing to remember is that we are expected to carefully judge whether those close to us are really Christians (and encourage them to examine themselves if we think they might not be - but do it gracefully)
But... when it comes to the crunch, we can't tell whether someone who professes faith in a biblical Christ is definitely not saved. It is not for us to judge (in ultimate terms anyway). We can still refuse Christian fellowship with someone who is professes faith though they are unrepentant, but it is not our place to say definitively that they are not saved.
Only God can separate the wheat from the chaff. The difference between wheat and chaff is the heart and intentions. Even someone who appears totally outwardly spiritual could be a clever wolf or an empty piece of chaff, hiding alongside the true wheat.
Leave ultimate judgement up to God, but be wise with your decisions. Especially about who you let to teach other believers.