When storing fabric, you should keep in mind how long you want to store it. Fabric composition is organic, and like storing precious documents, you should consider the elements. Moisture, sunlight are the primary factors. If you wash your fabric before storing, you remove the excess starch which deters little critters. But also consider that plastic containers emit chemicals that can affect the strength of the fibers if left in it for extended periods of time. Certain cardboard has a pH factor to consider which may cause leaching of the colors. Using these containers over a short time period won't affect the fabric much, but if you keep them for years and years, it may be something to think about.