At least in the US, the right fails on every single item on your list with the exception of taxes (Edit: actually, every item on the list, I forgot about tariffs when giving right wing benefit of doubt on taxes.)
Now that the right is in power, they are explicitly big fans of digital control and limiting free speech. The president literally believes he has the authority to shut up speech he does not like. He has exerted governmental pressure to get people fired, kicked out of school, and deported for speech. They are also not reining in government spending at all.
One thing you left out here was “to avoid sexist harassment.”
This is a huge, well-known reason why a lot of women avoid a variety of male-dominated hobbies and jobs. Men make those spaces hostile to women.
Do you suppose men would make those spaces more or less hostile to trans women?
Okay, cool. So we can agree that stuff like bone & muscle density does not give men an advantage in chess.
It is a much harder to quantify difference, then. Less objective, I think you’d agree? Like, the win rates are objective, but the reasons for them are less so. Making discriminatory policies based on something that is hard to quantify seems like a bad idea.
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One other thing that might give people, men or women, an advantage in a game like chess (or E sports) could be autism. This might sound like a joke, but it’s not.
And men have higher rates of autism than women. Exact rates are highly disputed due to stuff like sexism in some diagnostic criteria. But even trying to account for that men still seem to be more often autistic.
Should there be an Autistic League?
Note: Trans people also seem to have much higher rates of autism than the general population.
I do not personally think we should make any changes to leagues based on this info. But re: chess & esports, it seems like a more relevant thing than gender.