You can *soak* a cotton batting and you can spin it dry in a washing machine without damaging it. The reason they say not to wash is because any agitation at all will turn the batting into an unuseable mess. If you dry the batting in a dryer, the batting will shrink and you will not get the nice shrinking in the quilt that many people like with cotton. It is that kind of shrinking after quilting that makes old-time quilts crinkly and soft. If you pre-shrink the batting in the dryer, the quilt will be much flatter and without dimension even after washing.
Roxanne (sorry, famous quilter from Hawaii, can't remember her last name at the moment) swore by Fairfield cotton batting for her hand quilting. However, she said it was very important to soak the batting to remove the sizing in it that made it wonderful for machine quilters to use. She would soak it, spin it out, and I *think* let it air dry in order to make it very easy to hand quilt. It is not at all necessary to do this with that batting if you are going to machine quilt it.
Not all cotton battings have sizing in them. Each brand has its own way of manufacturing cotton batting. From what I know, if you are hand quilting, you need to be careful to stay away from cotton battings that are needle-punched with scrim. The needle-punching through scrim make them very stable and excellent for machine quilting, but it is more difficult to push a needle through the needle-punched scrim. Some hand quilters don't mind this effort, but I found it made a huge difference in how pleasurable hand quilting was. The Fairfield batt I mentioned above is not needle-punched with scrim, but rather manufactured with sizing to add stability for machine quilting. Removing the sizing makes the batting very easy to hand needle.
I haven't used every cotton batting on the market. The old-fashioned Blue Ribbon all-cotton batting I hand-needled I found, afterwards, contained bits and pieces of seed and boll, and also oils that made the needle stick. More modern manufacture eliminates these problems for hand quilters. I have heard that Quilter's Dream is a good modern all-cotton batting for hand quilters, but haven't actually used it myself.
I should add that all-cotton batting without needle-punching/scrim needs the closest quilting to stand the test of time -- up to 1 inch apart. The 80/20 batts (80% cotton) can be quilted a bit further apart -- maybe 2 to 3 inches. One reason the needle-punched/scrim cotton battings are so popular is that they can be quilted much further apart -- 6 inches or so. They are still all cotton, still can be shrunk inside the quilt to create the old-timey crinkly effect, but they don't need the close quilting. The problem I have found with them is that the needlepunching and scrim change the drape of the batting dramatically, making them more stiff. Many people don't mind this, but I like a softer drape and am willing to quilt more closely in order to use the type of batting that will provide this.
Mary