> No one is worried in the slightest about letting trans men compete in men's sport.

By and large for most disciplines, there's no separate men's leagues or men's competitions. So women and trans-men and everyone else is mostly already allowed to compete in men's sports.

See eg https://en.wikipedia.org/wiki/Judit_Polg%C3%A1r

> Traditionally, chess had been a male-dominated activity, and women were often seen as weaker players, thus advancing the idea of a Women's World Champion.[16] However, from the beginning, László was against the idea that his daughters had to participate in female-only events. "Women are able to achieve results similar, in fields of intellectual activities, to that of men," he wrote. "Chess is a form of intellectual activity, so this applies to chess. Accordingly, we reject any kind of discrimination in this respect."[17] This put the Polgárs in conflict with the Hungarian Chess Federation of the day, whose policy was for women to play in women-only tournaments. Polgár's older sister, Susan, first fought the bureaucracy by playing in men's tournaments and refusing to play in women's tournaments. In 1985, when she was a 15-year-old International Master, Susan said that it was due to this conflict that she had not been awarded the Grandmaster title despite having made the norm eleven times.[18]

> Or letting trans men into men's toilets or spaces ...

That one is interesting, because women's toilets are usually all cubicles, and men's toilets is the only place where you could actually see anything.. Btw, it's not just trans-men that get a free pass here, but cis-women also often go to men's toilets when the queue for the women's toilets is too long, and nobody bats an eyelid.

There's just very few sports in which the male body is not at an intrinsic mechanical advantage.

When you come from the extreme tail of the bell curve that elite sportspeople come from, that small advantage becomes a large advantage. When you move the mean a little, the tails move a lot.

This doesn't just affect trans women but also intersex women. There's a definite tension in sport insofar as we expect elite sportspeople to be abnormal humans far from the mean. For males this is unproblematic: an abnormally strong male like Michael Phelps or Usain Bolt is still clearly a male.

But for females nature does not provide for us a clear line but rather a smooth gradient between female and male. The difference between an abnormally strong female and an abnormally weak male is not a line that nature always provides for us, it's a line that has to be drawn artificially and is therefore open to debate and challenge.

> There's just very few sports in which the male body is not at an intrinsic mechanical advantage.

Yes. So it's interesting that even in something as cerebral as chess, men dominate.

One plausible explanation I've heard for this is that while men and women have the same average mental capabilities, men have a higher standard deviation than women. There there are more outliers in both directions. Champions are found at the upper extreme.

Well, there are more homeless men than homeless women.

(If that serves as an illustration of the other side of the bell curve.)

Regarding toilets, it is because women's toilets have also traditionally served as a 'safe space' (i.e. without men). It is somewhere they can go without being subject to (for example) what is colloquially termed the 'male gaze'. Hence the disquiet over trans-women using such spaces, and the lack of disquiet over the reverse.

Of course in a fully enlightened society arguably women should not need such safe spaces, but I'm not sure we are quite there yet.