That's why it's time to stop talking about all of this as a bulk category. Different situations care about different aspect of sex/gender.

In sports, it isn't really relevant what a person thinks about themselves. Gender is used as a proxy for expected performance envelope - you don't want to mix people with radically different characteristics, because that would not make for fair competition. I'm guessing that eventually we'll stop talking about "men" and "women" teams, and figure out new terms that directly reference the relevant biological characteristics.