Yes they do. After PE they do.
and if a boy says he is a girl inside, in California he can use the girls locker room
They're supposed to. They probably say they do. I'm telling you, I see it at my gym when the hockey and lacrosse teams come in for their core workouts and all: The kids don't freaking bathe before they leave.
And I don't think it's that they go home for their showers— 'cuz when they come into the gym before their workout, you can smell them coming!
My current theory is that they're self-conscious about taking off their clothes, because someone might think they're homosexual. Or someone might be homosexual. Nobody gave it a thought when I was a kid 100 years ago—when people were supposedly uptight about sex.