We went in November with my ds5 (now 6) which is allergic to latex and my dd23's friend who is allergic to shellfish. We had to talk to the chef at every table service restaurant. If it were a buffet, they took her up and explained what she could/could not eat and would tell her what on the menu to avoid. I found out that most restaurants at Disney do not use latex gloves for food preparation and at the few that do, the Chef made my son special meals and they brought out brand new napkins/utensils that had never been washed. You should have seen the plate they brought out for him at the Liberty Tree Tavern -- you could easily have feed 5 grown men. Now, he already had a dinner roll in his hand when the CM noticed the allergy on the card -- she literally ripped it out of his hand - he started to cry until Goofy came over to console him.
When you call to make your ADR's be sure to mention the allergies.
I asked at each counter service restaurant if latex gloves were used -- didn't happen across one in nine days that did.