This is entirely about political, religious, and social pressure attempting to limit social change that they strongly disagree with.
In a way it's like affirmative action. And like I've said elsewhere, when there's talk of inclusion, someone must be excluded.
Chess is open to all. Women's chess drives inclusion by exclusion.
The categories aren’t male and female, the categories are women and “open”, so anyone who wants to can compete in the open category. I’m disappointed they don’t consider trans women women because they are but chess having a women’s league isn’t that weird
Not really though. There are only two requirements to being a "trans woman":
1. Be a man
2. Call yourself a woman
That's it. Excluding them from women-only spaces is the only sensible policy if the essential character of such spaces is to be maintained.
Also at some point trans people look nearly identical to straight people so no one would even know the difference without scrutinizing records
Making an exception for the latter if they make some attempt to perform femininity, even if it's a somewhat convincing act, really just undermines the entire point.