To me, It sounds like they are trying to minimize their risk if these are indeed true allergies and not just typical intolerance's. It is not cool to expect them to carry all the legal responsibility for placing a child in an environment where their known allergen will be present.
I am required to serve milk. I am required to have a doctors release to not serve a child milk, by the state. Same as for enrolling non-immunized children or giving daily medications. It isn't personal.
Have you asked your doctor? It should be a pretty common request for them with patients with true allergies.