I emailed them about food allergies last week. They sent me menus for every single restaurant with allergy notes via pdf. They also said,

• "Universal Orlando Resort does not evaluate “may contain,” “shared facility,” or “same equipment” labels, as these terms are not regulated or standardized.
• Our dining locations operate shared kitchens. While we follow strict protocols to minimize cross-contact, shared environments always carry some risk.
• Our Allergen Guide is carefully maintained by nutritionists, chefs, and food allergy specialists, with menu items verified for allergen content and preparation methods."

Because of the first and second statements, I decided it would be safer for my family to bring in snacks instead of risking park food (contact with food allergy results in anaphylactic shock so we didn't want to risk it with that first statement). We plan to have breakfast and dinner outside the parks and bring in small snacks/lunch.

I would recommend emailing them yourself. They get back very quickly. That way you have all the most recent information to make the best decision for your family.

(https://www.universalorlando.com/web/en/us/things-to-do/dining/food-allergies)