I make things from washcloths (hand puppets, dust gloves, etc) and I always serge the edges because of the fluff that is generated when they are cut. I know that makes the seams bulky, but if you lengthen the stitch it isn't bad. I think if the pieces for the quilt would be large, it would be fine to serge. Small ones not so much. I sure wouldn't shave the terry! I also would not waste stabilizer. T-shirt quilts require it because of the stretch, but I don't see that being a problem with terry.