A slightly different twist on this thread, but highly relevant.
Dining with Allergies in WDW
Emily has a allergies identified as a FODMAP allergies, which essentially means she cannot have anything with any level of Fructose. As this is many things including Dairy and Wheat products, we just simply said that she had both Dairy and Wheat Allergies and threw in Onions as well.
The process for WDW is that when you make a booking for a Table Service restaurant, that you provide the information on the booking. Then when you arrive, you need to inform the server and they then make arrangements.
Informing the server isn't really necessary anyway, because the bookings have already got the information, but it's best to anyway. The chef then comes to the table and discusses what is available, asks what the person wants and then they come up with a compromise or solution that is safe. The chef then has to prepare the food them selves in the correct settings, ie separate to the other food and then the food is bought to the table separate to the other meals.
For the counter service options, it is similar. When you get to the front, simply inform the server person that you have allergies, and they go and get the chef. The chef comes out, mostly with a book, and then you decide what you want. The chef tells the server what to record and then the remaining order is taken. Chef will prepare the food themselves and bring it out themselves, no-one else is allowed to touch it.
We were worried about Emily eating, but whilst we were on a Disney property (including the Ship), she ate as well as we did, sometimes better! Taking a child or anyone with food allergies to any Disney destination (US) is a pain free, simple and worry free task.
The Ships are much better, they actually take your order the evening before for the next night and it is prepared separately and ready when other meals are. At the buffets, chef takes them around and discusses the ingredients of each dish and says yes you can or no you shouldn't eat something.