Table service have always been very accomodating when we have travelled with folks with various dietary needs. Even at buffets, we have had chefs prepare special plates for certain situations.
Counter service is a bit harder, as the kitchens there do not really have the capability to change recipes or produce off-menu items as easily as TS kitchens do. Here it may be a better option to pack lunches with things that are safe, and picnic in the parks rather than navigate menus full of things which can be decidedly not low-fat or low-sodium. There will be some options out there, like salads and such, which would work, but you'll need to do the research ahead of time and seek guidance from Disney dining.