I am celiac and had no issues at all with GF options on our trip.
Boathouse was great in DS - actually served fresh GF rolls rather than frozen ones that you get elsewhere on property.
LTT was my favorite dinner in the parks/resorts (outside of Shula's, but that's a different deal). Was not sure exactly what to expect with it being family style, but they brought out a completely separate platter for me that was entirely GF (including GF rice bread stuffing). Great meal.
We also ate at Cape May, Crystal Palace, Sci Fi, San Angel Inn and DLuxe Burger (carryout) with absolutely no cross contamination issues. Food at each was good, but nothing to get too excited about.
Shula's was also very accommodating and pretty easy to do GF. Obviously a different experience than most Disney restaurants with the price, but it was an amazing meal and they took my allergy pretty seriously. Waiter was very knowledgeable and helpful.
Also did Chef Mickeys for breakfast and it was great. On top of gluten, I also have a pork allergy, so breakfast can be a bit tricky. Chef came out and talked with me and made up a separate platter of entirely GF/pork free food that I could eat.
For CS, Flame Tree was a great lunch option at AK. Also had the GF chicken nuggets and fries somewhere in Magic Kingdom (can't remember where) and they were really good.
For me, GF options where I live are pretty limited, so anytime I can get multiple GF options somewhere it is a nice change. Hands down my best experience with food was Erin McKenna's Bakery in DS. Entire bakery is GF. It had been a long time since I had walked in somewhere and could order/eat anything and everything without even asking if it was GF. If you go to DS, it is definitely worth your time to stop by Erin McKenna's.