Don't be ridiculous. You really don't see a difference between someone choosing to see a doctor for their own benefit and the state forcing someone to be subjected to an examination for the state's benefit?

Nobody should accept gender discrimination or being touched without consent.

How far do you take that? One medical condition that has been considered militarily relevant is flat feet. If the state can draft people, can they make you show them your feet? If you can't avoid the draft but can avoid the medical exam, isn't that a way of avoiding the draft?