We ate there last year for lunch, and our DS *may* have a peanut allergy. (He's not been officially tested, but he had an allergic reaction about 3 years ago when he accidentally got a taste of his sister's PB sandwich. So, per doctor's instructions, we treat him as if he is allergic, & we decided to wait a couple of years to get him tested in the hopes he might "grow out" of the allergy in the meantime.)
Anyway, since he did have an allergic reaction to PB, we treat him as if he's allergic & we're very careful in making sure he doesn't eat peanuts or anything that contains peanuts (or any other nuts, for that matter).
However, I will say that, if he's allergic, he's not so allergic that he has a reaction from traces of peanut oil left on tables like some kids do, and he's eaten things that have been processed on machines that also process peanut-containing products, and he's never had a problem that I've noticed.
So we just make sure he doesn't eat anything w/ peanuts, and, if I'm not sure, I ask. At the Crystal Palace, there were so many choices on the buffet at lunch, that I never had to ask - fruit, chicken tenders, mac & cheese, green beans, carrots, bread, ice cream, and so much more. He had plenty to eat. And I don't recall seeing anything on the buffet that had nuts - w/ the exception of a couple of desserts & peanuts to sprinkle on sundaes - but I could be remembering wrong.
Anyway, we weren't worried at Crystal Palace and didn't have a problem w/ finding enough for our DS to eat. And he didn't have any reactions to anything he ate. Of course, I do think that, if he has an allergy, it's a slight one & not severe like some children, so take my comments for what they're worth.
The chefs at WDW restaurants are normally very accommodating. The chef at Akershus (Norway) in EPCOT sent out a special dessert for DS since all the desserts on the sampler plate had either nuts in them or were prepared too closely to the other desserts to be "safe". DS also got a special appetizer at Akershus.