Actually "sex" is what you are born with. Gender is how you view yourself psychologically. So the correct answer is just refer to everything by its sex. So women's sports are now "female" sports, and only accept female athletes. Problem solved.
Being male but feeling like a girl doesn't change the fact that you're a boy.
Sports have always been referred to as men's sports and women's sports.
Men's sports for male athletes
Women's sports for female athletes
If you want to compete on a level playing field form "trans athlete" teams. That way you will have males competing with males and females competing with females.
But wait - 😄 that is the way it always was.
If you're "trans" then you just gotta compete with the men while you are dressed in drag.
Fact is, mentally ill, narcissistic people don't want a level playing field. They want trophies and their "name" in records books to assuage their feelings of worthlessness.
Sources,,,,,,, really, you can find any source to confirm your biase. Rather than being a sheep do your own research. That is if you're smart enough to ask the right questions.