There is a clear distinction of sex, if you have a penis you are a man and if you don't have a penis you are a woman. This is how you should choose which bathroom you use. Are the schools going to provide security in every bathroom to make sure there is no inappropriate activity? This is goes against the rights of privacy for 99.9% of the students.
For the President to blackmail schools with the threat of funding cuts if they do not follow his policy is dictator like.