> We have somehow decided that chromosomal advantages are unfair
That somehow was mostly because people with certain chromosomal characteristics were heavily disadvantaged in sports, but increasingly wanted participation in them. Because those people (who we called "women") would largely be unable to be competitive and/or would face considerable increased risk of physical harm if they played in/against the same teams as everyone else, people with those chromosomal characteristics splintered off to compete in/against teams of themselves.
This was extremely successful and many women have been happily participating in sports, enjoying the ability to win games by virtue of their training and the non-sex defining aspects of their genetic make up, all without having to unnecessarily accept outsized risks of bodily harm and injury.
It's also worth mentioning that there hasn't been much effort to keep women from competing outside of their own divisions if they're willing to accept the lower odds of success and higher risks of harm to themselves that'd come from that. For the most part, they have been deciding for themselves that it isn't worth it.
It's not even as if chromosomal advantages are the only place we've done this. We have weight classes in certain sports. We have teams that only accept people within certain age ranges. We have divisions based on demonstrated ability. We even have things like the special Olympics. These really aren't a problem or a bad thing to have.
People can't choose their biology, but they can choose to play sports in a way that's more fair and safe for themselves and the others they play with and that's a perfectly acceptable practice that we should encourage. This is true even when it means that some people are excluded from specific teams or events because of things they cannot change about themselves. There are still places for pretty much everyone who wants to play if they look hard enough, even if not everyone is able to be a part of any team or division that they'd like to.