all the mainstream lines are on par when it comes to accommodating special diets. the general rule of thumb is you will order the next night's dinner the day before. all the buffets, all you have to do is ask for a chef to come out and they will walk you through every station pointing what is and isn't safe. that being said, many people with very severe reactions stay away from them altogether because people will invariably cross contaminate with the serving utensils.
they all have dedicated kitchens for prep and cooking to prevent/minimize cross contamination issues back of the house.
I have had two different friends, same ship at different times, same allergy( GF plus no dairy) one was very happy with the variety and taste of everything, the other less so.. found the GF options esp in bread form to be severely lacking in taste and appeal
My own personal experience on Disney was NOT fun. I have a mild shellfish allergy( I like it, it doesn't like me) . one of the soups one evening was a seafood chowder of some sort, so I asked my waitstaff if it was plain seafood, or if there was shellfish involved. he went back with the bowl, came back out with it and said it was perfectly safe.
it wasn't. thankfully I only had about 4-5 spoonfuls before I got a mouth full of shrimp so my evening wasn't totally ruined, just a few uncomfortable hours in the cabin that night.