Let the station worker know that you have an allergy. They will call a managing chef. The chef will prepare your order personally after conferring with you. They have gf buns and will make your fries in a dedicated fryer (different than the fryer on the line). I was impressed and was able to eat happily and safely for several days.
Did not have to be staying at Disney to eat there. The staff immediately called the chef out and the chef offered to make "just about anything" on the menu. We had pizza and chicken tenders with fries. All prepared separately and in a separate fryer. Was very good and we would definitely go back.
Quick serve with typical fast food, but options were tasty. Gf pizza is good, gf chicken tenders are awesome and a manager or chef always come out to take your order and serve it in a separate area. Better celiac knowledge than any restaurants at home.