I've been told the only folks who get to check under the hood most places are border control. Need to match your passport.
I'm told the US does issue passports based on current gender. And you can carry doctor's letters and stuff to explain to those countries you're traveling to. Which is what you need a passport for. Traveling to, not establishing gender here. Maybe we should eliminate gender. We're all the same anyway, kinda, and think of the discrimination actions we'd eliminate. Same with race. No gender, no race. Fewer lawsuits.