There is a reason the Olympics, the NCAA, and sports organizations around the country disagree with you. Have you ever stopped to consider why? It's because your assumptions about puberty are wrong. 

If you want to start campaigning for bone density classes in sports then I will certainly believe what you're saying isn't about prejudice. But you're going to have a hard time justifying having all the black women out there (who average in the male range) in their own class. It's going to look like prejudice to them too. And you haven't even come close to proving that bone density gives all the advantages you are assuming. Hence why arguments about bone density are so spurious. 

If you had studies showing there was a difference in physical performance for trans women, superior to that of cisgender women, then you would have something real. Until then, all you have is an argument tat isn't even half baked. 

These orgs didn't accept trans people on a whim. They had reasons you ignore