Well, they're also adding Man in Tuxedo and Woman in Tuxedo.
Pretty sure people don't become gay, bi, or trans by putting on a veil.
Tuxedo is fine - men and women both wear tuxedos sometimes, whether they’re straight or LGBT, with no offense intended.
I can’t imagine a man with a mustache wearing a veil for any reason other than they think it’ll be hilarious. Maybe I’m wrong - if somebody has seen such a sight, let me know.