You're right, and I was wrong before - the example of "If X was a true Y, they would do what I say all Ys should do" seems like it might be related to No True Scotsman but it's definitely different. It seems like the fallacy would be in the speaker's definition of "a true Y", so maybe it's using a "Persuasive definition"[0]? I'm not certain, but I'm also curious if there's a better term!

[0] https://en.wikipedia.org/wiki/Persuasive_definition