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This is such a difficult issue. No, transgender people don't choose to be that. Any less than a gay man or a lesbian. Of course, the world is so full of bigots. The corollary is that nobody complains when men enter what is considered "female" domains: nursing, beauty, wellness. Some are considered odd, but it doesn't stop them, does it?

Isn't it the human condition to want to be considered "normal"? Then we also want to be different. We can't win, can we?

It's pretty simple to tell if someone is legitimately transgender which is why I don't see it being such a big deal. Those people already have it difficult enough, I can imagine athletics or any hobby is a nice escape from the crap they have to constantly deal with. It's a shame they are getting hassled there as well.
Olympic athletes of all types are already so far removed from what a normal human is (edit: capable of ), I don't really care about their precise gender.