Part of the problem with the separate category is that FINA offered an "open" category because they restricted the entrance of transwomen swimmers to the women's events to only if they started HRT before the age of 12. This occurred in 2023 Worlds and not one person signed up. They are open to creating this category in the future.
Part of Riley Gaines and others who have spoken out is about how the NCAA treated the situation. They went to the 2022 Nationals and NCAA had made all locker rooms "unisex" meaning anyone could use the locker room, Lia Thomas, a transgendered woman, and men, meaning any coaches, doctors, trainers, etc could enter the locker room. This was done without athlete knowledge and they didn't know until they arrived to Nationals in Washington.
Some athletes were upset by this and changed in janitor's closets and other closed off spaces.
While there is definitely some transphobia happening, I can also take the point of view of some of the women not comfortable with the locker rooms now being unisex-especially without prior knowledge. Their feelings are valid as well.
NAIGC (NCAA clubs) has a competition already with no gender categories. Woman can do parallel bars, men can do balance beam, for example. Transman Wren Exley of UCLA was named Male Gymnast of the year. I remember watching a cis man compete floor to floor music, I am sorry I can't remember his name. So such non gender competitions are possible.