Here is a copy and paste from sheepskin com about the care of sheepskin. They advise agianst using woolite also. I do because it is at least a little more gentle on the wool than laundry detergent. They make a shampoo just for cleaning the natural sheep skin and it is available at sheepskin com. See below or
go to sheepskin com and look at care instrutions.
For auto accessories:
When it's time to give them a deep cleaning, we recommend either hand or machine wash with our Sheepskin Shampoo. Then allow them to air dry. We do not recommend Woolite or laundry detergents. Finally, fluff up the wool with a wire brush.