Ideally, we should consider everyone who is born again / born from above, and only them, to be Christians. Often people use the term "true Christians", and that's generally what they mean. Unfortunately we *cannot know* who is and isn't a true Christian by belief. According to James:
Jas 2:19 You believe that there is one God; you do well: the devils also believe, and tremble.
So there is a type of belief that does not save. Also, Jesus said there will be tares in the church, and we are not to attempt to remove them.
Since I can never be sure who is saved, it makes sense to treat people according to what they claim, and to some extent based on external evidence. In most cases it is best to treat people with the same consideration, whether they appear to be mature Christians, doubters, or outright atheists.