I think I had heard that the plastic verses fabric 'rumor' came from a sealed plastic bag that contained some moisture... thus the mildew!!!! I use plastic bins (not entirely sealed, as some air circulation occurs) and have not had any problems. I did have some problems years ago when my fabric was stored in my basement in dresser drawers and cardboard (which attracted and held moisture)... Duh! Mildew!
I'm now a plastic girl! and no more basement storage!