We traveled to WDW in May with our son, who has a gluten allergy. WDW is, 100%, the most accommodating place I've encountered for guests with food allergies. Every TS and CS has gluten-free food options. At every TS, the chef personally came to our table to explain what he could make for us, or to provide a tour of the buffet to show-off the gluten-free items. Chef Mickey's even offers gluten-free Mickey waffles. I never for a second felt that anything he was eating would be unsafe for him.
A few other thoughts:
1. For TS, call WDW Dining and add the gluten allergy onto your reservation. You can also email them a form listing all of your TS reservations, and they will make sure the chef knows about the allergy before your arrival.
2.
WDW Guest Services has lot more info, including a list of CS locations in each park that can accommodation food allergies.
3. CS meals may take longer than your are accustomed to because they cannot pre-plan for your arrival.
Others' experiences may vary, but I couldn't imagine WDW being more sensitive and accommodating to those with food allergies such as a gluten sensitivity.