There are no restrictions about the type of food you can bring to the park with you. You are welcome to bring anything you like: sandwiches, fruit, snacks, beverages, etc. You should be aware of that alcoholic beverages may not be brought into the parks. Nor are glass containers, other than baby food jars, allowed.
While you can bring any food you want to WDW, there are some restrictions about how you transport food into the parks. Large coolers and wheeled coolers are not permitted. If you click
here, you'll find a list of Frequently Asked Disney parks questions. At the bottom of the list, you'll see the maximum dimensions of coolers allowed in the parks. As long as you stay within these guidelines, you can enjoy your own food in the theme parks.
Have a great trip!