Your post is providing a very important warning and despite the fact that I try to think about this stuff when searching my own beliefs and while shopping for labels for myself, I surely don't mind hearing and being reminded of this warning over and over.
Still, I would disagree a bit with one of the labels you mentioned.
Someone can not believe in "God", but that doesn't make them atheist either, they can simply acknowledge they don't know as an agnostic.
The working definition I am using for the term atheist is exactly someone who lacks belief in a deity. It's a common misconception that an atheist would be somebody who would say "I'm 100% certain a god does not exists" while most atheists I know (myself included) use the term to represent their belief that the claim that a god exist hasn't met it's burden of proof. Back in the day, I used to call myself an agnostic atheist just because I could not rule out the existence of god with absolute certainty (as it seems to be impossible). Then I realized the agnostic part was actually redundant as an atheist is somebody that is not convinced that a god exists, not somebody that necessarily denies its existence with absolute certainty. I feel most agnostics fall into the definition I'musing for atheist, but I wouldn't go as far as telling people what labels they should be using as the labels as you pointed out are not the most important thing. There is indeed a spectrum and labels might often be limiting and everybody should be the arbiter of their own label and if they want to ascribe themselves to one at all.
That's why it can apply or not depending on how someone defines it. Etymologically, a-thetism is not-god and a-gnostic is not-knowing, so the distinction is evident on the word itself that is meant to convey the meaning in it's construction. But I get that it has changed for many to mean as you say it. Thanks for the feedback.