Any material that comes into direct contact with the CD has to be chemically inert. Materials like Vinyl use plasticizers to soften the vinyl. But softener agents migrate out of the vinyl over time and can penetrate the CD. These chemicals can dissolve the print on the CD and make the surface sticky. In some cases these chemicals eat through the polycarbonate of the disc and can destroy the CD. Also, plasticizers, specifically phthalates, have been classified as a "probable human carcinogen" by the EPA.
The playing surface of the CD needs to be protected not just against a chemical attack but also against physical impact. Sliding a CD out of a CD storage sleeve rubs the disc surfaces against the sleeve material and can leave micro scratches on the CD. Micro scratches can impair the quality of the play back and worst case make the CD unplayable.
All transparent materials made from e.g. vinyl, polypropylene and non-transparent materials like Tyvec, paper etc. will leave micro scratches on the CD and impair playback quality over time.
State of the art quality sleeves use non-woven fabrics made from inert materials like polypropylene that protect the CDs. However, not all non-wovens are created equally. Some fabrics will scratch the CDs and others will not. The fabrics may feels soft to the touch but that does not mean they will not leave micro scratches on the CDs.
A simple test is to rub a CD against the non-woven fabric with light pressure 10 times back and forth. Examine the disc surface under a halogen light that will reveal micro scratches.
The most effective solution is non-woven polypropylene fabric to protect the playing surface and matte transparent polypropylene for showing the graphics or printed side of the disc. This material combination is used in protective archival quality sleeves. Polypropylene also does not interfere with the graphics and provides protection for the printed materials as well.
An example of an archival quality storage solution that is using state of the art protective fabric and materials can be found for example in the CD Pro Sleeve from DiscSox.