I've been twice in the past two months. The staff will tell you that much of the menu can be made gluten free except the burritos and things like onion rings, fried calamari, etc. VERY IMPORTANT - THE FRYER IS SHARED and the staff does not seem to understand the importance of this fact - I was told that the chanclas are GF, but the base is fried in the shared fryer. So be sure to specify you do not want anything that comes out of the fryer if you are Celiac / concerned about cross contamination.
There are GF buns for the burgers (I have not tried them). The conchinita pibil and quesabirria tacos are TO DIE FOR (and GF).
— Somewhat
— No gluten-free information on the menu
— Some
— Excellent