Personal anecdotal experience, but I experienced my most rapid period of hair loss while taking creatine. This was for about 1 year when I was 22-23.

It could be underlying genetic predisposition to hair loss, but I do believe the creatine had an accelerating effect. When I stopped taking creatine, the rate of hair loss noticeably slowed down throughout the rest of my 20s.

Yeah, enough people say this that I avoid taking creatine knowing I have the genetic predisposition for male pattern baldness, despite the lack of solid evidence.

Although OP's post says "There is no mechanistic reason to think that would happen." but I don't think that's true. Creatine is known to increase DHT, and higher levels of DHT is linked to hair loss.