Lots of the below have gluten, but I'm including them just in case anything is of interest for the rest of your party. In general, gluten allergies and sensitivities are pretty easy to navigate in Disneyland, with safe options noted in the app for almost every location. I'd familiarize yourself with that feature before you go!
In Disneyland, my favorite sit-down is Cafe Orleans, which is arguably a better value than Blue Bayou and I really enjoy the real outdoor seating. For quick service, Docking Bay 7, Rancho Del Zocalo, Plaza Inn for the fried chicken, Jolly Holiday Bakery Cafe, and the different types of soup in a bread bowl offered at Royal Street Veranda and Harbor Galley are popular.
Disney's California Adventure has Lamplight Lounge (the downstairs restaurant that requires reservations, as well as the "Boardwalk Dining" bar upstairs that is walk-up only with a different menu). For quick service, all the restaurants in the San Fransokyo area have varied options, including Cocina Cucomonga, Aunt Cass's Cafe, and the Lucky Fortune Cookery. Paradise Garden Grill's menu rotates quite a bit based on the various festivals, but generally has good food.
For snacks and desserts, don't miss a Disneyland churro, found in various spots throughout both parks. Beignets at the Mint Julep Bar in New Orleans Square, and a corn dog in either park. There are lots of good cheesy carb options, including Cheesy Garlic Pretzel Bread at Edelweiss Snacks in Fantasyland, and the Mac & Cheese Cone in Carsland. Dole Whip, Ice Cream, and the Churro Toffee in various bakery cases. Pickles (spicy and regular) from various snack carts, and grilled meat and veggie skewers at Bengal Barbecue for a lower-carb, gluten free option.
