I have observed that will get you hired pretty quickly. Apparently the trick is to send the major a letter explaining the background discrepancy between your old name and your new name.

I don't know if they are falling all over themselves to be PC, or if they are just afraid of getting sued if they don't hire you.

But either way, gender is pretty fluid these days. Nothing they could do if you decided to transition back to what you started with down the road at some point. That point being after probation