Hi
Disney will accommodate a vegetarian diet in most restaurants even if it isn't something specifically on the menu.
My husband (a meat eater) wanted to go to O'Hana at the Polynesian. I didn't want to deprive him of having the carnivore feast that goes on there so we went. The chef came over to our table to ask what I do eat (no meat, chicken, or fish) and made me a vegetable stir fry with noodles. He even brought over the green beans without bacon on them for me.
So if someone in your party wants to go somewhere and you don't see something you like on the menu, just ask, and they can usually accommodate.
Also, the Plaza Restaurant in the Magic Kingdom has a good vegetarian sandwich on the menu with fresh mozzarella, tomatoes, hummus, pesto, lettuce, cucumbers, probably a few other things on focaccia.
Enjoy
Noreen