Y'know, if the person has what it takes to do the real job, without turning it into a platform for their personal social causes, great, I have no problem with it at all. What are the odds of that, though?
Call me biased if you choose, but this is a top-tier, very sensitive executive position, and I have reservations about the mental stability of anyone who has something as basic as their gender wires crossed inside the head (As opposed to people who have screwed-up glandular systems, who have perfectly legitimate reasons to fall outside the normal sorting tray).