This is going to be a bummer as you probably want the quilts to be seen but...
If you are going to store antique quilts in it, I would recommend wrapping them in acid free tissue and lining the cabinet where the fabric touches the wood with Tyvek. I would have serious concerns about anything that is giving off or have given off fumes. Gases still are given off that damage textiles, even though YOU can't smell them.
Also, I would line the glass with museum grade UV blocking film. It is completely transparent and won't affect the look. I have just had all the windows on my house done to protect my textiles and pictures. It wasn't as expensive as you would think.
HettyB