They may not want the comforters, blankets, or sheets in that form, but I bet they would like money. If you could get a group of caring people together that could craft the sheets into braided rugs, or pull toys for dogs, or beds for dogs and cats out of the comforters you could make a pretty good income to donate back to the shelters. It takes 3, 43-inch strips of fabric to make the braided pull toys for dogs. It takes 3 king size sheets to make a braided rug and those things alone would bring in some income. The beds are very simple to sew. To make the beds would require the most manual labor, but if you make square pillow shaped beds and stuff them with some of the comforter that is left over you may be surprised how good they look. If sewing by machine is too difficult you could use strong thread and a big needle to stitch them up.
Good luck to you.
