Looking at this as a religious issue and/or a separation of church and state issue is way too narrow a way to look at it, IMO.

To me, this is about whether or not a private school should have the right to develop their own ctiteria for accepting or denying admission to a student.

Religion isn't, or shouldn't, be the issue.

Suppose it was a school for the blind, and a kid who isn't blind wants to go there and is denied admission. Isn't that kid being discriminated against because he isn't blind?

Should a Catholic school have the right not to admit non-Catholics? Should a yeshiva have the right to deny admission to a gentile?

Wouldn't that be discrimination based on religion.

There are schoold for all boys and schools for all girls. Aren't they discriminating on the basis of sex?

Suppose a 45 year-old adult who never finished high school decides he wants to finish, applies to a private school, and is denied admission because of his age?

Wouldn't that be discrimination based on his age?

I bring up those examples because discrimination based on religion, gender, or age is illegal.