From which size is a country too big to operate as a single country? I think cultural identity is much more important than size, and the Chinese government has put a tremendous effort in culturally unifying the land with great success (and great cost; see Xinjiang, Tibet, Hong Kong, the relationship with Taiwan, loss of local languages and culture). I don’t see that disappearing anytime soon.
A civil war with a stalemate is of course possible (in fact it’s already the reality), but an USSR style collapse in many different countries is just not something I can see happen.
There are also women who have XY chromosomes, but they don’t have receptors for testosterone. They can even have very high levels of testosterone but it doesn’t do anything, why wouldn’t they be able to compete as women?
And why would having an uterus and being able to give birth naturally even matter? Are infertile humans not allowed to compete in the Olympics?