Certainly would be perhaps not illegal, but grossly stupid and incompetent to discriminate against a very competent pilot applicant just because he didn't wear a bra. This reminds me of an argument I had with the local postmaster once.
I had gone to see him to complain about us getting the wrong mail all the time. It was easy to see that the mail sorter was dyslexic because of the box numbers that appeared on the mail in our bag. I found that the person responsible was known to me and had a well known problem in this regard.
The PM told me he cannot discriminate against applicants and was bound to employ anyone. I said, "you stupid little bastard, how do you think I would go employing a pilot with no arms because of the same childish rule, the fact is this person has a severe disability which precludes her ability to do the specific task she is required to do, are you going to shift her on so we can get our own mail or do I go to a higher authority?"
He quickly changed the staff member onto something else, like sweeping floors or similar.