I thought it would be helpful to make a quick little list of food I'd suggest in the parks. So here it is!
Snacks & sweets- I've gotta mention that the dole whips, popcorn, and Mickey pretzels are all vegan, and are definitely favorites.
There are many different carts and stands in both parks that have fruits, veggies, hummus & crackers, and chips.
Rice milk chocolate bar, dark chocolate bar, and sugar cookies at candy palace & critter country shop.
Breakfast - Hash browns, or gluten free vegan Mickey waffles at Plaza Inn in Disneyland.
Pizza and pasta - it's not on the menu, but you can get vegan pizza in both parks in personal pizza size, or family size! Available at the Red Rocket Pizza Port in Disneyland and at Boardwalk Pizza & Pasta in California Adventure. Ask for it! At both locations you can order pasta (gf option) with marinara as well.
Mexican food - vegetarian tacos and taco salad (gluten free available) is available in both parks, at Rancho Del Zocalo and Cocina Cucamonga. Ask for no cheese or sour cream and you're good to go!
Bowls - Veggie gumbo at Cafe Orleans in Disneyland is vegan. (Ask for no crackers, they've got dairy)
Burgers - Chefs vegan burger at Carnation Cafe in Disneyland. Ask for the patty well done. Fries are fried in same oil as non vegan items, if that's a concern, get fruit!
Fine dining - Portobello mushroom and couscous maque chou at Blue Bayou in Disneyland. Vegan pasta or custom veggie tower (varies depending on the chef) at Carthay Circle restaurant in California Adventure.
Sandwiches - portobello & veggie sandwich (ask for no cheese or sauce) from Tomorrowland Terrace in Disneyland. Portobello mushroom philly (ask for no cheese) at Award Wieners in California Adventure. *UPDATE* these sandwiches are no longer available as Vegan.
Skewers - Veggie and tofu skewer at Big Thunder Ranch BBQ (frontier land) or veggie skewers and Bengal BBQ (adventure land) in Disneyland. Veggie and tofu skewer (get it with chimichuri sauce) with rice pilaf and pita bread at Paradise Garden Grill in California Adventure.
Healthier options - veggie and grain salad at Jolly Holiday on Main Street Disneyland. Ask for the side bread with no cheese. Vegan sushi in Carthay bar in California adventure, it's modified off the menu. Get it wrapped in rice paper.
Other favorites worth mentioning - chili pretzel cone (ask for no cheese) at Cozy Cones in Cars land - California Adventure (*UPDATE* Bread come is no longer Vegan. Chili is Vegan without cheese*). Tofu teriyaki, veggies and rice. Also edamame at Lucky Fortune Cookery in California Adventure.
These are just some favorites, but there are lots of other vegan and vegetarian options. So don't be afraid to ask your server! Happy eating!