"No atheist believes in God" is a factually correct statement. It's like saying "One does not equal two" - a verifiable, objective truth that does not rely on anyone's opinion.
Therefore, person B made a contradictory statement, and person A would be correct in responding "Then you aren't an atheist", because person B stated a verifiable falsehood. Same as saying "One equals two". We all know it's wrong.
Christianity has a much looser definition. You quoted it yourself:
A Christian (/ˈkrɪstʃən, -tiən/ ⓘ) is a person who follows or adheres to Christianity, a monotheistic Abrahamic religion based on the life and teachings of Jesus Christ.
So anyone who follows this religion and calls himself a Christian is a Christian. Nothing in the definition says "You must follow the Bible to the exact letter" in order to be one. There wouldn't be ANY Christians if that were true.
So that leaves us with a whole bunch of people who all claim to be Christian, but have different opinions on..
- how strictly you have to follow the Bible,
- whether racism is condoned or forbidden by the Bible,
- whether slavery is forbidden by the Bible,
- who you can fuck,
- what kind of funny hat you have to wear,
- what food you can or can't eat,
- whether you have to kill any non-believers,
... et cetera, et cetera.
And all of these people claim the others aren't the true believers.
Now here's a very simple question: What gives you the confidence, why should we believe you that it's YOU, out of all these people, who follows the correct interpretation of the Bible?
That's why the No True Scotsman fallacy applies to the whole bunch, including you, when you claim the others are no true Christians. Not a single Christian can objectively, verifiably prove that their individual view of Christianity is the correct one.