The reason athletic sports are segregated by gender is because physically, cis men vastly outperform cis women. Like, if we got rid of gender divisions altogether, cis men would be the only ones competing. I think it's unfair to both cis and transgender female athletes to effectively bar them from competitions altogether.

For nonathletic sports, it's more complicated. In chess, for example, the best female chess player in history is the 64th best chess player overall. The second best woman doesn't break the top 140. I assume this is because of historical discrimination against women in the chess community leading to them being underrepresented at the top. Having women's divisions is good because it encourages women to play.

To be clear, trans women are women, so it only makes sense to have them compete against other women.

Why are even non-contact sports segregated? Tennis? Why?!

This has been tested on multiple occasions

https://en.wikipedia.org/wiki/Battle_of_the_Sexes_(tennis)

The only real win in singles was Billie Jean King (then 29yo) over Bobby Riggs (then 55yo). Riggs had recently beaten Margaret Court who was a 17 year number one in the women's game.

Martina Navratilova in 2023 stated that the reason the 55-year-old Riggs lost to the 29-year-old King was simply because of age.[37] Navratilova said Riggs lost "because Bobby was too old," and added, "A 35 year old Bobby would have beaten all of us."[37]

Maybe bit it's more likely it's jus5 entertainment based. Women leagues are created to attract more viewers/participants.