Chess is male-dominated from childhood onwards, and the women who do play are highly outnumbered by men. So women-only chess clubs and tournaments are a way to try to redress the balance by encouraging women and girls to play.
How does it benefit women to allow men who say they have womanly feelings into such spaces? It doesn't - and that's why they are excluded, along with all other men.
Women's chess is a protected category. On that basis, FIDE are stating that women who don't want to be women can opt out of that category if they so wish, but men who say they are women cannot opt into it.
I don't think that is correct. What FIDE is doing is taking away titles earned by people who are now trans men that they earned when they played as women.
In international chess there generally aren't any men's competitions. There are competitions that are restricted to women and competitions that have no sex or gender restriction.
How does it benefit women to allow men who say they have womanly feelings into such spaces? It doesn't - and that's why they are excluded, along with all other men.