Because we limit attendance to people with child brains - not their bodies.

Au contraire, we limit it by AGE. A precocious child may have adult brainpower but we won't refuse them entry to school.
What your objective characteristics are, should influence what you can do in social contexts. Like age, or genitalia.

Tying it all back in, advocates for an expansive view of trans rights believe that (like elementary school) gender separation should be based on the brains of the people involved, not their bodies.

This is not an either-or. Trans advocates are saying that ONLY brains (psychology) should matter, observable reality (physiology) should not.

BTW I do admire your patience, notwithstanding our differences in opinions.

Like I said I don't know, and don't particularly care, about alternative sexuality (or genderness, whatever). I understand male/female, gay/straight/bisexual. Maybe asexual. That's as complicated as my tiny brain can grasp. But you mentioned that drag queens are men who think of themselves as men but dress in (traditional) women's clothes. I think most people would be uneasy to let such drag queens view their young daughters' bodies in locker room. What objective test can you apply to separate them from trans "women" (men who think themselves as women)?

BTW it is so mainstream for women to wear men's clothes, we don't even have a name for it. Is Hillary Clinton in a pantsuit a Drag King?

And are all Drag Queens queens or are there princesses, maids, peasants too?

Me stupid, me no understand any of this carp.