I wouldn't risk my career for a man, so why should I risk it for a woman? The rational thing seems to be playing it safe.
The whole situation is nuts
If you take the apparent maximally safe course of action at every turn in life, you probably won't achieve much. It's risky to change jobs, to break up with your current partner, to start dating someone, to have kids, to buy a house, to change cities, to pick a college/major, to pick an initial career, to drive in the rain, to play recreational sports, to travel to a different country, to eat sushi, and 100s of other times in any given year.
If you are willing to do something important (and work-related) for a man that you are not willing to do for a woman, IMO, you should not be in a position of leadership.