I recently traveled to Disney World and Universal Studios in Florida and I found that the restaurants in both parks were very accommodating to my food restrictions. When I asked about gluten free options the staff would invariably call over a manager or a chef to work with me to make sure my food was safe. It was a little more time consuming, but very helpful. They even had gluten free hot dog and burger buns available, so I wasn't having to eat a completely different type of meal as the rest of my party.
I hadn't really expected to be able to dine at either park, so it was a welcome surprise that I could have something other than the gluten free protein bars which I had brought with me. (By the way, it turns out protein bars are the same density as C4 and a half-dozen of them in your suitcase will cause the TSA to want to look in your bag.)
I just wanted to share my positive park experience.