I am a celiac and sometimes bring my own snacks to Disney. I always have snacks when I travel too. In the US we have tons of bars but not all are created equal in flavor lol. My favorites are KIND (mostly nuts and dried fruits so get sticky but don't melt in heat) and Luna bars (lots of yummy flavors- coated in chocolate so not good for heat). I think the best bread that is widely available is Canyon Bakehouse. Udi's is available in many places but sometime has holes and the flavor isn't the same. Nuts can be surprisingly hard to find as they are often sorted in the US on equipment as wheat (trail mix?). I find plain nuts at Trader Joes or a brand available more places is Wonderful (Pistachios/Almonds etc). I feel like raisins aren't filling so I don't bother with them. Enjoy life is carried by Disney themselves as they are top 8 allergen free and can be easily found nowadays too for all sorts of snacks. Peanut butter and GF crackers is an option, but pack in a plastic container rather than bag so they don't get crushed. Pretzels are widely available GF now and handle better than chips (less bulky too). US brands I like are Gratify and Glutino.
If I am eating the snack shortly (such as breakfast while at RD) I bring in string cheese, apple slices, carrot sticks, and celery slices if I can get them in their own bag. Whole fruit like apples, bananas, and oranges will last longer. There are also some meat jerky brands that are GF. If you plan on stopping at a store I can let you know how good their selection may be. Pantry items can also be bought online at a place like
Amazon and shipped to the hotel. There is a brand called Go Picnic that sells these boxes that are a collection of small snacks and select boxes are GF. The entire box for me is a snack, not a meal, though. I have bought these before travelling when I don't have time to gather a collection of GF items for the plane ride.
We have decent labelling laws here, if it states GF it should be below 20 pp in testing. Just read labels as we are in a phase where everyone wants to have GF items and some brands are making mistakes in a rush to put that on the shelves of stores (labelling something with wheat based soy sauce as GF). I truthfully also don't trust some brands as they have had recalls for making mistakes with their products and I feel like there are enough proven brands out there that specialize in these foods.
Also if you do QS meals you can often substitute the side with a bag of fruit or veggies that they give with the kiddie meal (for ex. get a bag of grapes with your sandwich instead of fries). When on the meal plan I do that to stay healthy and sometimes the cast member is relieved as they may need to bake the fries to make them GF which can take awhile. There are actually some fantastic QS places if you are GF (Sunshine Seasons and the sandwich at Be Our Guest for lunch was huge).