I quilted one quilt on a longarm with a minky backing, and didn't have any problems with tension or minky fur coming through to the top. My quilt top was all cotton, my thread was 40 wt cotton in both top and bobbin, and my batting was cotton. You do have to watch the stretch in the minky. I mounted it with a side which does not stretch so much across the top (and then bottom, too, of course). The stretchier sides were to the right and left side as I faced the quilt, and they do tend to roll under the way knits do.