Easy, he threatens to withdraw the federal money.
And the schools will cave post haste over the almighty $$$$$$$.
First, if the states are already accepting funds for agree-upon purposes, it is coercive and unconstitutional to withdraw all the funding by adding new provisions.
Second, it is Congress, and not the President, who sets the purposes of the funding.
So the SCOTUS ruling on the Medicare expansion of Obamacare should be precedent to stop Obama from using federal funding supplements to schools to coerce them into accepting new bathroom political policies.
-PJ