Chess is special case. Women are allowed to play in men torunaments. Not reverse. There are even special rules (since 1976) which specifically says that women cannot be prevented from participating based on gender (it wasn't clear to Indians at this time). Some (Judit Polgár,Vera Menchik) almost never played in woman ones. Chess rating system didn't take take gender into account but in 1986 active woman chess players excpt Susan Polgár got small bonus to rating.

There is research from 2007 ( https://onlinelibrary.wiley.com/doi/epdf/10.1002/ejsp.440 ) which shows that if is via Internet and women thinks their opponent are men - they show worse results. If gender is not known to both sides - results are mostly same.

It's not currently clear if M2F transgenders should be allowed to play in women competitions.

This is one of the weirdest for me, because there's literally no barrier that can justify this separation. And GMs like Hou Yifan for example can go toe to toe with anyone now.

In theory there's no reason. Yet aside from Yifan and Polgar there is no women GM which could go toe to toe with the top male GMs. The same is true historically.

It is unclear why, this requires further research - the Chess world decided to just roll with it and have separate tournaments.

You can't just make stuff up. Hou Yifan says herself that chess is very exhausting and men have an advantage in this aspect.

"I think there is a physical aspect because chess exhausts a lot of energy, especially when games last 6-7 hours, and here women could be more disadvantaged."

Why deny differences in biology to further a false reality?

https://www.chess.com/article/view/hou-yifan-interview-chess

You mean the same Hou Yifan who said multiple times that she was speculating?

I'd trust the world champion of chess to not mention physicality as a possible reason unless it had merit. She's been playing chess her whole life.

I'm not disagreeing with her opinion or negating her experiences, it's not my place. That said, classical (3h+) isn't the only form of chess, and it could be something that is personal to her and not representative of female players as a monolith.

Logically speaking, it's still a disadvantage even if it's one that matters less in some scenarios. Gender is highly predictive of a lot of biological statistics. Truly, we should be basing brackets on the biological stats themselves and make gender segregation a thing of the past. How will people react when the brackets reflect genetic potential rather than gender potential? Probably just as oppositional. People hate being told that someone else has a higher potential than them even if it's true. I don't blame them. But we can't live in a reality where we pretend that some aren't better built for certain endeavors.