I have a couple food allergies but always feel very safe when dining at Disney.
At each of the table service restaurants you will be given a menu which shows the acceptable food allergy lists. It makes it very easy to order.
If you are not comfortable with this you can ask to speak with the chef. This takes the stress out of dining.
if you would like to see a copy of the buffet menu from Crystal Palace from last month with the allergy list please email request to me at firstname.lastname@example.org I will be happy to send it to you.
Enjoy your meal!!