I'm in the laundry room, too and have my stash in plastic bins and smaller pieces in plastic sleeves or wood shelves. I had all my material on a wooden shelf and have heard that you shouldn't but I didn't have any trouble with the material. I have been collecting it for a number of years and inherited a lot from friends who did as they pleased. Maybe it has something to do with interactions over time or the work room environment but I have not had any issues.
It is, however much easier for me to see what I have and to carry a bin over to my cutting table when using plastic. I don't keep my lids on for the most part and am happy with the change.