If playing sports was essential to living to everyone across the board, yeah, they would be prohibited from being selective.

Trans people in school/collegiate sports resulted in a lost US election for the Democrats (sports scholarships are a thing). That's how important it is.

And no, I don't think that the advanced education is essential. General education is, but not advanced courses. And of course, everyone absolutely deserves a fair _chance_ to get the best possible education.