She's already been indicted on federal charges for hacking. Not being allowed to fly wouldn't be the main issue if she found her way into an American airport or airliner.
If they truly don't care to perceive a gender then a 50 / 50 pick. When I look at it's picture I honestly couldn't tell you if I perceive more male or female so I would've done same as op and picked one randomly and then for consistency not change it, even if some unrelated party tried to confuse things by making me change it.