For anyone with food allergies or food sensitivities, dining at any restaurant can be a nightmare, but not at Disney properties!! In fact, Disney takes allergies so seriously that it is a major factor as to why I keep going back to a Disney property year after year. I have been to Disneyland and Walt Disney World multiple times along with Disneyland Paris and more Disney properties are on my bucket list!
I had to remove all gluten from my life at the age of 34 after being diagnosed with Celiac disease. I was able to experience all Disney foods prior to my diagnosis. In my experience, restaurants outside of Disney don't take gluten too seriously. They have "gluten sensitive" menus, but good precautions are not taken in the kitchen. They share the same prep areas and fryers. The number of times I had to settle for a salad due to lack of options is countless.
BUT, at Disney, people with food allergies get the VIP treatment. Almost all Disney restaurants offer an allergy-friendly menu. I say "almost all", because some restaurants are just not equipped to accommodate people with allergies. For instance, I cannot have fish and chips in England at Epcot, because they don't have a separate fryer for gluten-free food and do not have gluten free batter.
Almost all restaurants will have a menu with what they can do and what they can substitute for the many different allergies such as fish, nuts, tree nuts, shellfish, soy, eggs, corn, lactose, milk, etc. You can also request to speak to the cast member who is trained with food allergies at Quick Service locations or the chef at a Table Service restaurant. While menus are ok, I strongly recommend to talk to a chef at the Table Service restaurants, because they will recommend what is best on the menu. I have also been lucky to get some "off the menu" suggestions! It would be prudent to take such careful precautions in order to avoid a negative outcome. I had a dish brought to me with crispy wontons on the top of my dish last Fall, which is a big no-no for me and they had to take it back and re-prepare all over, again.
Disney does not have a separate kitchen, but they do have a separate prep area and separate fryers. Some locations will make allergy-free Mickey waffles at breakfast time! Eating at a buffet? No problem! My favorite restaurant is actually Crystal Palace. The chef will personally come to your table and tell you what you can have from the buffet. Then, they will bring the food directly from the kitchen so there is no possible way of having any cross contamination from the spoons. Because it's a buffet, they will bring more of the foods you can have/want directly from the kitchen as much as you want.
Be prepared to wait for your food a little longer. I have waited as much as an extra 15 minutes at some Quick Service locations, but it is worth it. Out of the last 10 trips to Walt Disney World with Celiac disease, I have not been sick once. I, certainly, would not want anyone having to take time out of their long-awaited Disney vacation by having to go to the emergency room!
One last piece of advice, you can list allergies when making your dining reservations online or by telling the cast member over the phone if you prefer to call to make dining reservations. See the pictures below of what to expect to complete when making dining reservations online. It is on the last page under "Special Requests" right before you finalize the reservation and click "Reserve". If you have multiple food allergies, an allergy not already mentioned above, have a metabolic disorder, Phenylkeutonia (PKU), etc., I recommend you email or call the Disney location you will be visiting after you have made all of your dining reservations and at least 14 days in advance of your arrival date. The contact info for Walt Disney World and Disneyland are in the pictures below.
By the way, I think it is important to mention that asking for low sodium food is much more challenging. It is not considered to be an allergy. Disney considers it to be a lifestyle choice. Some table service restaurants are able to accommodate, but, for the most part, it is a difficult task for them to fulfill.
Wishing you a magical vacation free of allergy worries!!