I think if the rag quilt was made with fleece it would be okay. The fleece has no fibers to come off and it is really strong. If the cotton fabrics had short rags (1/2 inch)I don't know that they would be a problem either. I have done Chenille baby blankets and that fringe is about 1/4 to 1/2 inch long and I have never worried about a baby sucking it off.