Disney says
Summer, spring, winter or fall—doughy park pretzels are always seasoned to perfection.
Friendliest.app says
All pretzel carts sell bottled beverages. If you are sensitive to any of the listed allergens, it is recommended that you purchase drinks from another location with less chance of cross contamination.

Disneyland Pretzels are purported to be produced by J & J Snack Foods.

Allergy-friendly meals at Pretzels at small world Promenade