Good point on sports, not sure why I didn't think of that immediately. (Perhaps because, in all honesty, a very small minority of trans people are involved in situations like this, although they get a fair amount of attention.) After a couple of years on estrogen, though, trans women have lost most if not all of their strength advantage. I agree that this is a hard sell especially when we're talking about athletes at the more elite levels and in contact sports. I'm a little bit conflicted about it too, to be honest. This makes me a glad I'm a trans man, because no one will ever argue that my 5-foot-tall self would have an unfair advantage in men's sports :-)
With locker rooms and restrooms though, most trans people are exceptionally careful to not make it possible for anyone to tell that they're trans, or else they avoid these situations entirely. Any (supposedly) trans person who is out to antagonize other people in that kind of situation is clearly in the wrong, in my opinion. In the US, at least, most people aren't ready for co-ed restrooms and locker rooms, and may never be. That's neither good nor bad, it just is. Everyone, including trans people, have to live in the society that we're in. Some steps are just too big, and that's one of them. It's unfortunate that a few people's actions have really screwed things up for an entire community of people in this regard.
I'm curious: Do you object to trans women (or men) being in the women's (or men's) locker room if they're not visibly trans? Meaning, do you object to it on principle, or only to the "spectacle" that some people have caused?
I'm genuinely asking, I'm not trying to be sarcastic or draw you into any kind of trap.