Atheism is defined by us as the position that God does not exist. But some people who claim to be atheists and also believe in gods presumably define it differently. Are we justified in saying that they are incorrect, and not atheists?

If so, we are also justified in saying that people who claim to follow Jesus but do not are not Christians, regardless of what they think.

I'm not, I'd say that definition is silly. I think we should be able to say people aren't in a particular group even if they say they are.

Obviously there isn't a universally accepted criteria for atheism either, because there are people who believe in God who claim to be atheists. Why is a universally accepted criteria necessary?

But are they still an atheist if they believe in God? If not, then someone who doesn't actually follow Christ, but still claims to, is not a Christian.

Is that really true though? If someone says they're an atheist and yet believes that God exists, should I say they are not actually an atheist?