You can still have yeast breads without gluten. Many folks are confused with whether yeast has gluten in it, it normally does not.
The problem is not just the grains or the storage, but insidious cross-contamination. Celiac disease is like radiation poisoning: Every time you are hit by gluten, the damage becomes cumulative, it rarely if ever fully heals unless caught very very young. Eventually the intestinal villi just die off and do not regrow at all, leaving you without the ability to digest dairy products and metabolize many nutrients. Somewhere around that time, a number of autoimmune diseases ranging from cancers to arthritis also trigger--and don't go away. So celiac is not a case of "Oh, I had explosive diarrhea today, I'll be all right tomorrow" it is a case of every time you are exposed, you come closer to permanent and potentially fatal damage.
The situation doesn't have to be all that black,the trick is, to be very very careful about keeping your total "radiation" exposure down, for life.
Cross-contamination is a bitch. If you eat oats (which are safe) they are normally rotated in fields with wheat, so there is always some wheat content in "safe" crops like oats. (Barring some farms that take great pains to not rotate and to use totally separate mills.) When flours are milled, one mill and one set of millstones are typically used for all grains--more contamination.
Potato chips? All cooked in the same oil, if one batch of BBQ chips has wheat as a binder in the spices--they're all contaminated now.
Order a safe order of scrambled eggs in a diner? No, that's not safe either, if the diner just grilled a cheese sandwhich on the grill there's gluten in the grill oil, your eggs just picked it up unless the grill was rinsed down. Chinese food in a wok? The leftover soy sauce from the meal prepared before yours is a contaminant.
It can take a LONG hard sleuthing job to figure it all out. And, as little as five years ago, this was all almost unknown--even among physicians and internists.
Corn tortillas pack well as an alternative to travelling bread. They also remind you of why Mexico failed to conquer the world. (G)