Plastic is one of the cheaper material which is probably why you keep running into more of it. I try not to store any fabric in plastic as sometimes it will absorb the smell of the plastic especially if you live in a warmer climate. All my fabric is stored in a walk-in closet on open shelving for the most part. For organization purposes, I do use a lot of smaller see-through bins from the dollar store, not for fabric unless its short term. I love the canvas bins but you can't see what's in them. What is it you are trying to store or are you just looking to get away from plastic?