What will they do when @ChaimMoskowitz chooses the female one
That's small change compared to people who choose their gender on a daily basis. They might have to limit the availability of those seat blocks based on residential zipcode (with some serious challenge questions required in order to avoid fraud).
Alternatively, just like they do for the TSA (and other airport security agencies) pat-downs, they can designate a male and female checker to verify based on objective criteria below the waistline.
And if indeed someone is caught selecting a seat assigned to a different gender, that person would have to pay for a seat elsewhere.