Chess is one sport where I didn't expect transwomen controversy to even be relevant -- physical abilities don't even come into play.
There are women-only competitions to encourage more women to play and to give them some visibility, but it's not the same premise as separated sporting events, that women have an inherent disadvantage.
There was a lot of good discussion about gender in chess a few years ago when Queen's Gambit was released on Netflix[1].
1. https://theconversation.com/whats-behind-the-gender-imbalanc...