To answer my own question, I'm torn. I believe that a parent's right to feed their child as they please (or really, control any choices for their child's life/health/well-being) ends when they start significantly and measurably impacting the other students in the kid's class. If the food they are eating makes them overhyper, resulting in bad behavior and interrupting the class, that's fundamentally unfair to all of the other students.
It'd be very hard for the school to define that "line", though, or definitely show that it was the food contributing.
My friend the Kindergarten teacher handles this by teaching nutrition to her kindergarteners, having them talk to their parents about healthy lunches, etc.