For purposes of this post I will use "male" and "female" to refer to gonadal sex as a biologist would, to avoid confusion, rather than words like "men" and "women", except in the context of the phrase "womens' teams" because that's what they're currently called.
Extensive research has demonstrated a
staggering, huge difference between males and females - that is, male advantage - in most kinds of athletic performance. The strongest difference is in upper body strength, but females have ~20% less lower body strength on average as well. An important factor I also don't often see mentioned is that the female hip structure, in order to accommodate childbirth, is less efficient for walking and running by a surprising margin. However, there does seem to be a difference in liver metabolism, which doesn't look like it's been studied very much, which seems to make the curve flip in ultramarathons where energy storage becomes more important than physical ability. Still, that's not what most people typically think of as an athletic advantage, and it doesn't apply in any of the cases I have ever heard people arguing about. Even amateur sports teams of boys under 18 regularly beat professional women's teams in matches - I hear this is often done in soccer, like this example:
https://www.cbssports.com/soccer/news/a-dallas-fc-under-15-boys-squad-beat-the-u-s-womens-national-team-in-a-scrimmage/See for example:
https://law.duke.edu/sports/sex-sport/comparative-athletic-performance/https://link.springer.com/article/10.1007/BF00235103https://journals.physiology.org/doi/abs/10.1152/jappl.1991.71.2.644https://pubmed.ncbi.nlm.nih.gov/17186303/I've also heard completely unsourced claims that female joints are more flexible, supposedly giving female athletes certain advantages, but this appears to be a complete lie, since joint injuries are far more common in women than men:
https://www.health.harvard.edu/blog/the-gender-gap-in-sports-injuries-201512038708 ; the reason for this seems to be that female joints
are indeed less
stable, meaning they move more easily, but
not more
flexible, meaning they can't accommodate this greater range of motion without injury. Joints may also become more flexible during pregnancy, so that the pelvis can expand; but I don't know of any studies testing how this applies to athletics, and I'm unclear on whether it actually means a reduced injury rate either, or just a wider range of motion.
There have been occasional "studies" by "researchers" that claim to find things that literally every middle school gym teacher knows aren't true - that there's no performance advantage between males and females - but this is absolutely not the scientific consensus, and these studies just don't replicate, because they're not real. Parapsychologists keep churning out studies finding evidence for psychic powers, too. It's motivated reasoning.
Why not "And Trans should be allowed as human beings with equal rights and equal protections, unless and until it is scientifically proven to a reasonable scientific consensus that Trans enjoy an unfair advantage necessitating that their rights to their own identity should be invaded in the interests of fair competition?"
Well, it has been. Also, what is a "right to one's own identity"? That's a silly concept. Would you be okay with keeping the same structure, but renaming it to "genetically male" and "genetically female"?