They do a pretty good job. If you tell them that you have a gluten allergy they will change their gloves and give you a burger in a bowl or a lettuce wrapped burger. Fries are gluten free. Just pay attention and make sure they change the gloves, as I'm not sure if they've done that every time we've been here. We are not a celiac family, so I can't speak confidently as to whether they are celiac friendly or not.
No