Gluten free hamburger and hot dog buns seem to be fairly common at both parks, as are gf pizza, pasta and dedicated friers for french fries. I never get to eat any of that stuff so it was extra special to eat a hamburger and french fries at Disney!
A lot of the breakfast places also have a "fun" gf option (instead of the normal eggs/potato/bacon) like gf pancakes at Carnation Cafe for example!