As others have said, they probably don't in things that are prepared from scratch on site but anything that comes from a supplier probably has it. It is almost impossible to find ice cream without it, for example, and I seriously doubt Disney is making their own.
We avoid it at home out of personal preference not necessity, so when we're out I don't make it an issue. It would be tough for people with real sensitivities, though, since it is in most breads, sweets, and sauces.