I would venture that it likely depends on the cookware and the cleaning methods. I wouldn't be too inclined to share cutting boards, cast iron, enamelware, non-stick stuff (inevitably scratches), stoneware, metal pans, or anything with "nooks and crannies." (the cast iron & enamelware I'd be protective of just because they'll well outlast the roomies!) So, about the only shareable thing- glass. Whoops.
Since realistically it's unlikely that the roomie will consistently distinguish between these classes of goods (your roomie may be better than those I have/have had), I'd probably just flat-out ban them if I had, say, celiac. If I could tolerate small amounts of contamination- I'd probably still ban them but be less of a hard-nose about it (meaning- less likely to keep my cookware in my room after the first time I see them using it).
Roomies are weird; it's ok to be the weird one.
Oh! You might want to look into resources about keeping kosher- I'm thinking there may be some way out there (a superhandy non-toxic way, unlike, say, sharpie-markering things) to mark GF cookware, since those who keep kosher might have to mark their cookware in similar situations.