I go to this In N Out at least a couple times a month. I always order the burger protein style burger which means without buns and wrapped in lettuce. To be honest I prefer the lettuce wrap more than most gluten free buns ( most crumble and have the texture of cardboard). I also order the fries that are prepared in a dedicated fryer. I have never had an adverse reaction to this meal. It's pretty darn tasty.
I got a double- double and fries. I told them I had an allergy and to change their gloves. They made a note. I also asked for no grilled onions and sauce packets on the side to avoid CC. It was delicious, and I did not get sick. It was my first time trying, I think like any fast food joint it’s all dependent on the staff at the location.
As all In N Out locations I have been to, I have never gotten sick at this one in Escondido and the people working there are always very careful and considerate. I feel as safe as anyone can in a non-dedicated dacility. We often even go here over our local dedicated GF location because the burgers and fries are better and cheaper (and we don't eat burgers and fries for health..). Just make sure to order each item with "allergy to gluten". For the burger, the only GF alternative is "protein style" which means lettuce instead of a bun. If you specify gluten allergy they prepare it in a separate area with clean gloves etc.