I have never seen “hermaphrodite” on any government form. What do they put down?
It’s an edge case. Does a government form determine reality? They can put down one, both, none.
You cannot put down both or none on any government form that does not consider gender to be a non-biological thing.
Laws are not supposed to be selectively applied. If they can put down whichever one they choose, you are admitting your definition of ‘man’ and ‘woman’ do not apply to how society works.
I know “the exception that proves the rule” is a fun phrase, but it’s not actually how things work.
But this is a biological thing. It’s a medical condition. It’s not your gender if you were born with both sets of organs. The point of equality was to get rid of laws being selectively applied. By your philosophy, race also works similarly. Someone who is latino is whoever says they’re latino.