Transgender man wins women's 100 yd and 400 yd freestyle races.

You're getting very hung up on this

I'd presume it was phrased that way, using males instead of men, for clarity.

There probably is I am sure. But it is surprisingly difficult to identify and find any.

Take snooker for example. I was surprised recently to find that World Championship Snooker at the Crucible is actually not a Male only affair. It is entirely open to the Female Sex too. So I googled a little and I found stuff like this:

https://www.quora.com/Why-are-women-not-competitive-with-men-in-snooker

So while there are some acknowledged barriers to why women are not as competitive or numerous both historically and at present - it's still true that mentally and physically the average male and female are not on the same playing field even in something as relatively laid back as snooker. It is a surprisingly physically and mentally demanding game. And physical advantages exist in things like height too. There is nothing in theory stopping any woman from entering the World Snooker Tour and arriving in the crucible and lifting the world championship trophy. I simply do not expect to see it in my lifetime however.

So while there may exist sports where equal competition between the biologically binary sexes of our species is possible I can not think of one off the top of my head. Lawn bowling is a sport I know literally nothing about. Perhaps that one?

Yes indeed - that is what I meant when I wrote "So while there are some acknowledged barriers to why women are not as competitive or numerous both historically and at present". There are barriers there socially and historically which mean Women have been less likely to compete in great numbers. Including the things you just listed. Not least of which it has just been historically a guy thing culturally.

They are discussed at length in the links I put in the post above. But there are women competing in it. They just do not attain very high levels in the world rankings. And even if the number of women competing multiplied 100 fold over the next decade and money was thrown at it - I would not expect them to eviscerate the rankings either. But I would look forward to being corrected on that. More women at the Crucible would be great to watch.

Do not underestimate chess either :) One of the reasons given for why women have an issue at snooker against men is the length of the matches. The sheer gruel of hours long play at the highest levels (First to 18 frames in the world final for example - after grueling days of play just to get to that final in the first place) is very physically and mentally demanding. Chess no less so for the same reasons. Chess might look like simply sitting in a chair relaxing to the uninitiated. But I have seen people collapse after an intense game and I have one friend who on occasion wins competitions and having done so goes home and sleeps for 20 hours straight. It's _ exhausting _ and any physical advantage is going to play into that.

And archery is something I engage in both for sport and at times in hunting. A powerful bow is highly physically demanding. If I go out and practice for an hour or two tonight - I will have serious muscle aches in surprising places tomorrow. Muscles I did not even know I had in the past hurt when I first took up the sport. And if competition is long enough that physical fatigue sets in then that will play into your mental accuracy and your ability to line up a shot and more. I have a oneida kestrel bow for anyone who is into that kind of thing. I have killed targets with it and I have killed animals with it. It is not an undemanding pursuit.

I would be wary of your phrasing though where you wrote "can be done by both". I doubt you meant anything by that, it is just how you wrote it. But to be vicariously pedantic - which a lot of people on a thread like this can often be - I would be the last person who would suggest any sport can not be done by both. Specifically the question is about them competing against each other. But I struggle to think of any sport on the planet that can not be "done by both". They all can. Including MMA which is probably one of the most physically demanding sports on the planet. Short of Penis Fencing (please tell me this is not a sport hehehehe) I would like to think there is not a single sport on the planet not open to female participation and competition.

Typical male physical advantages would absolutely be a factor in those you listed, except chess.

Height and reach are huge advantages in snooker. The tables may look small on television, but they're just under 12' x 6'

Being able to consistently use heavier balls with a hard throw, and more grip and arm strength to generate more spin are advantages in bowling.

Height and reach are advantages in darts too. The bullseye is 5'8" from the floor, so would be above the majority of women's heads.

Shooting and archery would depend on the height of the targets and how long the competition went for, but typically a male frame would take more strain.

Even things like motor racing, the stresses put on the body is why there has only ever been 5 women F1 drivers, and none since 1992. 29 starts between them.

I’d say it’s a lot easier for a man to practice ball and table games at the pub than it is for a woman to practice at a pub - at least without routine harassment. Lot of social barriers to entry in the sport, easier for males to have a lifetime of frequent experience playing the game.