It's clear, though. The distinction is atheism or not. By understanding what an ism fundamentally is, you're able to distinguish what it is not. Someone cannot adhere to an ism based on a thing without knowing what the thing is first.
It's a distinction of 1 or 0.
I had assumed this was clear enough response to your questioning.
And it's not a disagreement, really. This isn't an opinion of mine, it's one of the cruxes of the English/Latin language. It is the reason the -ism suffix exists. Your statement is simply incompatible with what any word ending with -ism is. A newborn cannot be any of them.