Travelling with a food allergy or sensitivity can be difficult. Disney has worked to reduce the stress by making chefs visits to your table easier as well as incorporating allergy and sensitivity requests in the Advance Dining Reservation system and providing allergen information on menus at many Disney restaurants.
And for a while now, Disney has been moving toward incorporating food allergy and sensitivity orders into the Mobile Order System in the My Disney Experience App.
After you scroll down past the standard menu, the allergy and sensitivity options appear.