It will depend a little on what level of school we're talking about. If you're looking at a junior school, with children of just 5 years old, then banning nuts is far less unreasonable than at a secondary or high school.
If by the age of 11, (or thereabouts, whatever the age is in your country) a child cannot be responsible enough to avoid their particular allergen, then are they really mature enough to be in the school at all?