I store all my fabrics in plastic bins with tight lids. I've done this for many, many years and have never had a moment's problems with my fabric. I replaced all my plastic bins after christmas because they stacked better in my sewing room and did not find even one spot. I never have however stored fabrics in plastic grocery bags so I would not know what results you might get. Silica crystals placed in plastic bins will help with any moisture problems.