Light issues is why I've kept my fabric in cardboard. Cardboard has some issues you should be aware and should never be stored directly on a cement floor and should be temperature/climate controlled -- it will wick up moisture and that can encourage/attract mold and bugs and such.
I think so long as it is not stored in direct light of a window, I'd get some archival tissue paper and simply line your plastic with that. Here's some examples:
https://www.amazon.com/acid-free-tis...er+for+storage