Chromosome pairs are not the determination for sex at birth. That's a thing we tell children because it's easier to understand. There are intersex people with different sets of chromosomes than that, and also with the chromosomes but the "wrong" sex. What determines sex is hormones during development. It's associated with chromosome pairs, but that isn't deterministic. This is why the conversation is so hard, because hormones determine everything, and we have the ability to control hormones now.

Also, sexual differentiation for physical ability only really happens during puberty. Before then, male and female children are identically capable. Considering that, where do puberty blockers or other hormone treatment land when used before puberty in this conversation? Also, where does long term hormone treatment land?

This whole thing has been overblown and not properly understood because some people have an agenda to turn people against trans people, and it's an easy target. Sadly, sex doesn't work based on their child level understanding of it, and the people pushing it have no incentive to expand anyone's understanding, and likely not their own either.

Edit: I also want to add that hormone testing isn't a great idea either. The captain of the Zambia soccer team was disqualified because her testosterone levels were too high naturally, despite being born female and birth and not doing anything to change things. It turns out that everyone has testosterone and estrogen to varying levels, and physical ability changes drastically from person to person regardless of hormones as well. This topic is so much more difficult than the simple solutions some people propose.