The states have never delgated to the feds, via the Constitution, the specific power to regulate either intrastate commerce or any aspect of public school policy. Here's evidence of that concerning intrastate commerce.
”State inspection laws, health laws, and laws for regulating the internal commerce of a State, and those which respect turnpike roads, ferries, &c. are not within the power granted to Congress. [emphases added]” —Gibbons v. Ogden, 1824.
Unfortunately, they are accepting federal funds for school lunches and agree to certain "strings" that come with the $$$.
I don't like it, and don't think it should be happening, but alas, it is.
Now if we could just get USDA to put the same stringent restrictions on those receiving SNAP (food stamps) funds s they are putting on children in schools.............