After a few click-throughs, here is one of the studies they reference. I always had a feeling this was a bunch of bullshit. Many schools won't even allow students to have peanut butter sandwiches in their lunch these days. But if a parent says that their kid will die if exposed to PB&J, what's a principle to do? Say that they are batshit? Hardly. Parents are batshit, but you can't say that. And, another side effect is that these kids are going to grow up being afraid of everything, because their moms are uneducated and neurotic.
I've always had a feeling it was a bunch of bullshit too. I have a relative that won't let her kids eat many common foods. The older child had some sort of sever reaction as a small child and the younger kid can't eat it just in case. Also, not letting peanut butter in to a school is just craziness. I remember in kindergarden our daily snack always involved peanut butter. It's a perfect food for a growing kid. How else you going to get a kid to eat celery?