I know very few people that don’t have a good ‘quirk’ that would probably seem strange to many others.
For instance, DH can’t eat a sandwich with only one filling, FIL detests cucumber so much that if a salad is being served the cucumber has to be placed in a separate serving dish and I have not eaten meat since 1998 and also choose to not eat food that has touched meat, raw or cooked. It might not bother some vegetarians but it does bother me. I don’t like the idea of it and I think that’s what ‘psychologically alergic’ was supposed to convey.
I respect DH and FIL and accommodate that, even though I think they’re both a bit odd, because I respect their right to choose what they eat. It’s not up to me to dismiss others eating habits and food preferences.
For myself, firstly I loathe discussing being a vegetarian. I just am, it’s not fascinating, it’s just a fact. Secondly, I am responsible for what I consume but I think it is fair enough to include asking people to avoid putting meat on my food is a reasonable part of that. And if they don’t respect that I don’t eat the food, whether in s restaurant or at home. It is MY choice and does not impact on anyone else.
And in the case of the OP and her DD I don’t think she’s asking for anything strange but, as I said before, needs to help her daughter to articulate those needs, or as others have suggested, provide alternative food.
But I stand by my initial reaction - it is not unreasonable to have your own feelings and wishes on what you consume and nor is it unreasonable that her DD has been upset by these incidents at school, however trivial it might seem to others.