The billy bookcases are 11" deep (outside measurement). So the inside shelf depth is probably about 10 1/2 inches. If your fabric on boards is less than that depth you would be ok. There is a wide selection of doors available for the Billy bookcases. That is what I originally wanted but realized that my bins (containing UFO's) would not fit on the shelves.
I went with IKEA wardrobe cabinets (PAX) and the child's wardrobe cabinet(stuva). These wardrobes are too deep to do fabric on boards efficiently. So I have ruler folded fabric and stacked them on the shelves. This is not quite as convenient as having them on end like bolts - but the wardrobes also have room for my bins of UFO's, an antique sewing machine, dies for my Sizzix Big shot pro, etc. And everything is behind closed doors - so neat (except for the overflow due to more fabric acquisition trips, LOL.