Love that the chef comes out and talks to you before you order food!
We ate at: Chef Mickey's for character breakfast, Flying Fish (Boardwalk), Coral Reef (Epcot), Le Cellier (Epcot), Portobellos (Downtown), Yachtsman (Yacht Club).
Quick Service was: Flame Tree BBQ (Animal), Pecos Bill's Cafe (Magic), Sunshine Season (Epcot)*, they would sub out the unsafe cookie for a 2 pack of enjoy life cookies. Also the good news is the PB&J sandwich they served was an Uncrustable so it was pre-packaged and not made fresh around other foods.
*was a little disappointed in kid friendly main dishes since all bread is considered cross contaminated. They did have lots of a la carte items such as chips, whole fruit, grapes, carrots, enjoy life chocolate bars.
For breakfast we grabbed quick things to eat like cereal and yogurt at the market in our hotel complex. I did see a few allergy safe items for sale...divvies popcorn (this was the only place I saw any divvies), surf sweets jelly beans, and there was some sort of gluten free brownie (didn't read ingredients on this one).