The “American” one would suggest “an autistic”, rather than “an autist”, no? He is American, he is an American.

This may be an issue with English not differentiating precisely between most nouns and adjectives relating to countries. In my head "an American" is clearly a noun but that might be me. Better examples might be "a New Yorker" or "a Londoner".

I’ve said repeatedly that this isn’t a settled debate within the autism community, and at no point have I suggested that other people aren’t free to use whatever terms they want

You did say you don't want to accept a term just because it's popular and I was agreeing to that. The fact that we're talking about this seemed to suggest to me that you felt at least some pressure to conform to what everybody else is saying.

I understand that. I’m specifically talking about the English word “autist”. Ich rede nicht über Deutsch.

And I was drawing parallels between two very closely related languages of two closely related cultures. The words "autist" and "Autist/Autistin" are obviously related so it's interesting to see if there's differences in how they're used and what they are.

I suppose that asks the question why is “autistic” one of (if not the) only example with a dedicated noun?

Language is under no obligation to be consistent and logical. Speakers of English for some reason didn't see need for dedicated nouns here and they dropped out of use (or never developed in the first place). Why English doesn't have a word for "doch" is beyond me but here we are. English also doesn't have dedicated nouns for "person from [country]", as we established above. Does that mean anything profound in particular? To my mind it suggests simply that English somehow tends to prefer adjectives.