DS and DH are both Celiacs. When you are at the TS restaurants, there is absolutely no problem at all. The chef will come out and talk to you. They are wonderful. If you are at a buffet, the chef will walk with you through the buffet and tell you exactly what you can and cannot eat. Dessert is pretty limited at WDW. They will offer ice cream, some kind of frozen bar, or the old stand-by GF brownies.
At the CS restaurants, the service is good, but could be better. When you are ready to place your order, you need to say the word "Allergy". If you say gluten free or celiac they will look at you like you are speaking a foreign language (and unfortunately for many CM's you are). "Allergy" is what they are trained to act on. They will get you a manager and he/she will show you a book and explain your choices. BE PREPARED TO WAIT for your food. It will take at least 20-30 minutes to come out. Often the person you ordered from (usually the manager) will hand deliver it to you, but it takes a quite a long time because they have to prepare it special when you order.
My "boys" love to go to WDW because they have so many options and are treated so well. The TS restaurants have got this GF thing nailed. CS need to work on it still.