I posted a thread recently asking about using comic book boards to store fabric. I wound up buying magazine boards instead, because they're slightly larger. I bought 1000 boards from BCW -
https://www.bcwsupplies.com/magazine-backing-boards - and have used 800+ so far. These boards are buffered and certified to be acid free. They're also coated on one side, but it's the buffering that counts for fabric since we use both sides of the board.
I had previously folded my fabric around a 8.5" ruler and stored it in stacks. It took quite a while to re-fold around the magazine boards, and I used these shirt clips to secure the fabric edges, top and bottom -
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1. (Thanks to marjben for suggesting them.) I like the way my shelves look now, and I think I will be more likely to use what I have (rather than buy more) since I can see it better. So now I've said it, yes, I'm on a fabric diet!
Before and after pictures -