Our baby charity ties most of their quilts. I'm not sure how a baby can get their fingers involved with the threads, as the threaded knots are of either pearl cotton or thicker crochet thread; and are about 4-6 inches apart; double-looped and tied with a square knot and then one more knot (left over right, right over left and then again left over right) They are washed and the remaining threads are about 1 and 1/2 in. long. These are utilitarian and seem to hold up well to numerous washings. We, too, use poly batting and ONLY cotton fabrics.
We use the 9-patch one yard baby quilt and the tying seems to work well with the seams, pattern and size.