Overall, I'd strongly recommend the Yucca Tree Eatery, with a few caveats. When we arrived, the host was able to answer our questions and mentioned the option for gluten-free bread for sandwiches. We emphasized concerns about shared kitchen space and cross-contamination (two of our party have celiac) and the host said that different portions of the grill are used for different items (chicken, buns, etc), with the grill being cleaned regularly. We ordered the chicken bowl, as that looked like the safest lunch option, and it was very tasty. The meal was affordable, and the portions were good for lunch. Neither of us felt sick at any point after the meal, and the Yucca Tree Eatery easily seemed like one of the safest restaurant options for celiacs on the northern side of Joshua Tree, where it has felt exceedingly challenging to find reliable dining options.
Also, the pineapple water is excellent, very refreshing after a morning hike. I'd definitely return again for breakfast or lunch.