And this right here shows how much of Bingo you are to focus on who you're calling a
male instead of the biology of people with XXY chromosomes. Because by their genetics their XXY chromosomes means they typically have undeveloped testes which produce
less testosterone and develop less muscle mass than average males. You may want to classify them as male but they are at just as much disadvantage and risk of injury competing with average males as an average woman would be.
Why not?

I don't actually care how you decide to designate sports leagues I'm just pointing out the way you want to do it is stupid and demonstrably counter to what you claim your concern is as I did just above.
If you understood the science then you wouldn't want XXY males competing when XY males if you concern was testosterone levels.