There's nothing in the Constitution preventing the school from doing as it pleases. However, there's also nothing in the Constitution guaranteeing the school's religious tax-exempt status. They want to act like a typical private organization? Fine, they can pay taxes like one.
They're acting like a religious organization.
If you think they should be punished financially for requiring students to keep to the tenets of their religion in and out of school, I wonder about your real motives.
But fine, tax their asses off. Maybe the government would like to then cough up the money that won't be available for the hospitals and charities that the Catholic church won't be able to afford to run anymore.