That's fine, so far as it goes.
But it is not up to us to decide who is, or is not, a Christian -- to do so, is to judge something that is in neither of our job descriptions. You did that, though .... which is a bit close to what Paul warns us against.
Let’s say you enter a room full of people that you have known for some time. You are feeling particularly evangelistic. You decide to share the Gospel with one of them. Which one will you approach?