I have washed Warm and Natural batting in my washing machine.
I cut the pieces into slightly oversized pieces to allow for shrinkage - soak them in hot water for about an hour or so - and then wash them gently for just a few minutes and dry gently.
In fact, I had to wash one piece twice because my cat peed on it!
On the other hand, I put something that was *not* warm and natural in the washing machine - and it ended up being like tons of washed tissues in the washing machine. So - read the directions.