Find GF and other allergen info here: https://madmex.com/menus/
I've been going to Mad Mex forever. Their food is amazing. It's hard to order the gf options online unless you do pickup, but ypu can ask for corn tortillas instead of flour on most things.
I'm very gluten sensitive and not fully celiac, and I will eat out of the shared fryer so I can't comment on what that experience is. But I've never had issues when I specify that I can't have any gluten ingredients.
— Somewhat
— No gluten-free information on the menu
— Most/All
— Excellent