Last I checked, the Mickey bars were produced in a facility that also processes nuts or peanuts (cannot remember which).
There are many safe options for people with peanut and tree nut allergies to eat in the parks. Many of the regular menu items will be safe as well, and chefs or managers can confirm ingredients in anything on the menu. The list you have been sent is for special ingredients available to the chef to substitute when the original menu item may not be safe. They can also be used for special requests for people with allergies. (For instance, if you prefer Tinkyada pasta to regular pasta, you can order it at places that have it as an optional ingredient. Or the Namaste pancake mix can be used to make Mickey waffles in kitchens where regular waffles or pancakes may contain or may be made near nuts.) We've had wonderful meals at the parks with multiple food allergies. Don't focus on this list so much, but it is good reference when you need a snack - you can see which place will definitely have something safe (like Enjoy Life cookies). Be specific about your allergies EVERY time you order so they take appropriate precautions to prevent cross-contact with nuts or peanuts.
There are some thing on that list that I wouldn't deem safe for my own peanut and tree nut allergies because they are made in shared facilities but may not be labelled as such, like the ice cream - we have not found ANY ice creams in America that are made in dedicated peanut and tree nut-free facilities. Tofutti and Rice Dream both make nutty flavours on the same lines as their regular ones. So use your own judgement and comfort level when ordering those. Same for Silk soy milk - they make almond milk on shared lines and I've had reactions to that before it was labelled as such, so we avoid that too. (Silk isn't always on the safe foods list, but I've seen it before... apparently all soy milks in America are made on shared lines with nuts of some sort, so we simply avoid it all.) We deal with extremely low tolerance levels and instantly severe reactions, but you can decide for yourself on what you are comfortable with. Otherwise, everything else on the list should be safe. Disney takes allergies very seriously!
We've had pizza from Pizzasafari. The fact that it isn't on the list means they don't have any alternate products there to work with. If you ask the manager, they can bring out a binder with ingredient labels for the items you wish to order and determine whether it will be safe or not. They made our pizzas on new pans and it took longer than normal, but I forget why... could have been because we ordered our pizza without cheese, or maybe it was the sauce we couldn't have... whatever it was, they were able to make safe pizza for us and we enjoyed it, although not our best meal in the park. (It's very basic pizza, not what we're used to.)
Note the allergy on any reservations you make, and mention it at every dining establishment you visit. Even Disney resort restaurants are able to accommodate allergies. Enjoy!
