I think the issue is that in the ‘was gay’ sentence, there’s an implication that the person used to be but is no longer. So we use the present simple so that misunderstanding can’t be made

Simon has explained why it’s not “was” You can use either “did” or “do”. “Did you know” meaning “did you learn it before right now”, or “do you know” meaning “are you aware now”. In either case, your awareness is there in the present moment.

My pleasure. I agree that it’s a confusing grammas point because using was implies the past tense. So if we say ‘I thought he was a teacher’, it does implies he used to be one but isn’t any longer