My kitchen is a "shared line". My two teen boys and my wife eat gluten in the house so there's always a risk.
This has always been my line of thinking. If I want something that is guaranteed 100% safe, I eat an apple.
I do think, though, that in the first stages of healing, avoiding any CC is the best way to go. Now that I've been gluten-free for 5+ years, I have a little more "give" when it comes to CC.
I have also read in several different places that the FDA requirements for cleaning the assembly lines are so strict that it would be rather rare (not unheard of, just unlikely) for gluten to survive the cleaning process.