In general Disney is absolutely fantastic when it comes to allergies. Two of my family have a gluten allergy and Disney is one of the only places they can dine easily, almost like a normal person.
Having said that, there are some CMs and restaurants that seemingly did not get the memo. Our last trip to Le Cellier was a disaster - our server told them that they could only eat a plain steak with no sauce or sides. She refused to get the chef, after several times of asking, and made it crystal clear that we were a huge inconvenience being there. In the end we walked out without eating. This despite having had a reservation for months, and giving them advance notice of our dietary restrictions.
My point is that however good Disney is in general, you still have to be careful. Some servers (inside and outside of Disney) either wrongly think that they know everything (e.g. "there's no gluten in brown bread") or view it as a lifestyle choice or preference (on the same level as "I don't like mushrooms").
I realise that it sounds like a bit of a rant against Disney - it's really not! Once again, Disney are in general amazing when it comes to allergies.