See the 1990's VMI and Citadel instances of gender and admissions policies, for details about that little catch in "private" versus "federal compliance."

There are very few educational agencies that are truly "exempt" from federal laws intended to protect those in protected classes (disability, race, gender). Oh, there are agencies that THINK (or will say) that they are-- but a church preschool that runs a USDA lunch program? Yup-- they are obligated under the law because they accept funding from the feds. smile

Schrödinger's cat walks into a bar. And doesn't.