I've read this five times, and I can't parse it, something isn't clicking. Can you try elaborating or rephrasing please?
Damion's point is just that telling you someone is trans makes it slightly easier to identify them than if you didn't know. From a bayesian perspective I think that's valid. It may not be all that much information, but its information.
If you told me that the person I was trying to find in a crowd trains powerlifting, I'd probably find them faster than if I didn't know that, because I'd keep my eyes out for a particular type of physique. It wouldn't be 100% accurate, because some people train more than others and you can still have some skinny guy who trains twice a month. But it's still information.
Still, I don't think we should include people's hobbies on their ID, even if that information is potentially useful.
Aside from it being noisy information, there's also the issue of abuse. People can lie about their hobbies and they can lie about being trans. Its not entirely clear to me what the scenario is where we're meant to be using the information on someone's ID. I assume in most such cases the person
wants to be identifiable, like when a cop pulls you over, you want them to be able to identify that yes, you are the person on the ID. But if there are any adversarial situations, where people don't want to be identified, then listing hobbies or self-ID gender, is an opportunity for people to choose to be
less identifiable. I'm not sure this is an actual issue, but it does seem worth mentioning.
As I said, I think the main issue is just that while there's some information there, it's noisy and not particularly useful. If a male is wearing makeup but in their ID photo they aren't and their ID just says "Sex: Male", I don't think that adding "gender: feminine" would be an aha moment for the cop. The person handing over the ID can just say "yeah, I'm trans".
I can't really think of any situation where including gender on an ID would actually be useful.