So your stance is that you want to check people's genitals before they can play a sport, and that intersex people can't play? Don't either of those things feel a little off to you?

Just because people want to segregate doesn't make it okay. As a society, we've created loads of laws to make this exact point. It's why (e.g.) the country club restaurant has to serve black people. You can't segregate based on things a person can't change. Sometimes you can't even segregate based on things a person can change, like their religion.

Trans and intersex people need to be allowed to participate in sports. If we, as a society, are going to choose to differentiate sports teams based on gender, then we must allow these people to play based on the gender that they are.

If that's such a problem, we could also ban segregating sports teams based on gender. That's cool too.