I keep most of my fabric in plastic tubs and like the other gals who posted above, I am in it so often that there is plenty of air flow. As long as you are into your rubbermaids often I don't think it would be a problem. Although Rubbermaid probably seals a lot better than my cheap Walmart bins. If that's the case, I'd probably just crack the lid to allow for air flow and not worry about it. Hope that helps.
Plastic bins and shelves crammed full of washed, neatly folded fabric are my mainstays, but I must confess I have an enormous amount of blue fabrics in a huge, messy pile on my floor. I'm using them for several different quilts (all scrappy) and it's just easier to leave them out rather than folding them and putting them away just to take them back out again. I figure no one but me and my hedgehogs go into my quilt room (husband ventures in only when he has to) so only I see the messy pile. :P
~Tiffany