Imagine this conversation:
"Hey, remember that 'basketball' game we invented?"
"Yeah, what about it?"
"Well, lots of people are playing it, but some of them are unhappy."
"Oh no! What's wrong?"
"Well, they say they're not winning."
"Hm. Well, by the rules of the game, only one team can win, so... maybe we should split the sport up into different divisions, based on skill? We can use the Elo-like algorithms to determine which teams should play each other so that each team has a good chance to win."
"Well, we don't want to do that- it sounds a bit complicated to implement in practice. And, see, there's another thing."
"What is it?"
"Taller people tend to win more. From the stats, they have a big advantage, and it just makes sense if you think about what playing basketball well requires- being taller really does make you better at the game. A lot of the players who aren't having fun are shorter- they feel like they don't really have a fair shot at winning, just because of their height, which is something they can't really change."
"Ah! So you want to split the players up based on their height. Well, we might have some unwanted second-order effects from that - since we aren't accounting for things like muscle mass or aerobic capacity, anybody who is disadvantaged in those attributes might still not feel like they're getting a fair shot. But if the main effect really is height, then I guess-"
"No, no, no, we don't want to do that, either. We want to do it based on genes."
"Oh! Well, that's a bit tricky- loads of genes might affect height, and even more probably affect how good somebody can be at basketball- but maybe with enough data we can build a model to roughly determine somebody's 'innate' basketball ability, and split players up based on that, instead. Now, we need to be careful, because this won't take into account things besides genetics- say, early childhood environment- that folks could reasonably argue are outside of their control- but I guess it could be a clever solution to the pr-"
"Well, that sounds hard. So we want to do it based on whether somebody has two X chromosomes or only one. It's correlated with height, and height is correlated with innate basketball ability."
"But if you care about height, why not just split players up based on height?"
"Well, there are other factors related to basketball ability, too. Not just height, that's a straw man. And many of them are correlated with how many X chromosomes players have."
"But you brought height up... Well, okay, maybe a weighted combination of different metrics that affect basketball ability? Seems like that might be easier than doing genetic testing on everybody."
"No, we're not going to actually do genetic testing on everybody- honestly, that just sounds invasive and creepy. We're going to look at other attributes that correlate with how many X chromosomes players have, and we can usually guess how many X chromosomes they have that way, without having to test. If a player wants to do genetic testing to prove how many X chromosomes they have, maybe we'll let them do that, too. But mostly, we'll guess based on things like their facial structure, voice pitch, whether they have breasts or not, and their genitals."
"But none of those things directly affect height, much less basketball ability, to any meaningful degree! You're measuring a proxy of a proxy."
"... Well, that's what we're going to do."
If what you care about is basketball ability, try to split the sport up based on that, based on actual wins and losses. If that's too hard in practice, and what you care about is height, then split the sport up based on height. Don't segment based on some second-order proxy measure- that's just sloppy. And, honestly, it makes it a bit hard to believe this is actually some high-minded concern for fairness- it starts to seem like it's being motivated by something else.