The location on 6th street is NOT safe for celiac. The location on Massachusetts street IS safe for celia.
Everything on Chipotle's menu is gluten free, except for their flour tortilla. All of their meat is safe, as well as all of their add-ins. When I go, I ask for them to change gloves, and they are always friendly about it.
I usually get hard tacos or a bowl, so they prep everything in the clean bowl, not on contaminated surfaces. I have never had any cross contamination issues.