The U.S. govt has no right to interfere with any aspect of public education, neither institutionalized nor irregular. It is prohibited for the govt to fund a school, advertise education services, impose standards or requirements in any way related to public education, limit educational activities in any way shape or form (for example: by demanding licensing).
A teacher has an absolute, unrestricted, unalienable right to choose his students as he sees fit. A teacher is free to enroll and dismiss students on a whim at any time without answering to anyone or explaining his motives. The right of a teacher to freely select his students can not be limited by any institution, this amendment overrides any contractual obligations in this regard.
Simple as that. No more laws and «departments» and «committees» are needed. You can even send your department of education to a re-education camp in Siberia.
And by the way, these two clauses are sufficient to return MALE teachers to the schools.