The point, though, is that equality is a thing only when things are equal. You are still allowed to discriminate when it actually does make a difference.
It's even in the employment laws. It's called a bona fide occupational qualification (BFOQ) in the US, or bona fide occupational requirement (BFOR) in Canada, or genuine occupational qualification (GOQ) in the UK. The LGBT community can suc... err... look it up.
E.g., you can't prefer whites to blacks or viceversa to operate a crane, because that makes no difference to pulling the levers. You ARE however quite within your rights to only hire whites to play the role of Lincoln in a movie, or conversely to only consider black actors for the role of Mandela or Rosa Parks. Because the colour is an important part of that role, and does make a visible difference on film.
E.g., you can't discriminate by age when hiring an accountant, but you CAN if you're shooting porn or a high school drama.
It seems to me like if in sports the categories are based on the biological differences between biological men and biological women, then yes, it is the same thing. One can jolly well discriminate in that case, and idiots moaning about it being discrimination are just too stupid to be having that argument. Even if they happen to be LGBT.