I will concede that this issue is complicated.

However, I'd like to note that sport is fundamentally not "fair", however you define it.

If it is supposed to be about "the person who does X best wins" there would not be gendered leagues or weight classes or doping regulations, and there would only be one champion per sport who would die of performance enhancement drug overdose shortly after winning.

If it is supposed to be about "everyone gets an equal chance at winning" it would be a lottery.

Fundamentally ("the purpose of the system is what it does"), professional sport is first and foremost about entertainment and not fairness. Humans like to watch other, more skilled/fit humans do stuff, this is why we have all those competitions in the first place. There needs to be a component of skill/effort and unpredictability for it to be an interesting competition to watch. The reason gendered leagues, weight classes, paralympics etc exist is for representation of those classes of people in this (very important) genre of entertainment. Which is awesome.

However, what becomes obvious is that by denying trans athletes the chance to compete with people of their gender, you are denying those trans people representation of their identity. I also understand that in this particular situation, allowing trans people to compete could take away representation from cis women which I understand and is a valid concern of a disadvantaged group. But (at least from my cis-male perspective, so take it with a grain of salt) it generally doesn't, because there are very few transfem athletes, especially at professional sports levels, and years of transitioning generally take away enough of their performance for it to still be an interesting competition between AFAB women and AMAB women.