The soap that came to my mind, which I actually have used is not certified organic, but is natural, biodegradable, and never tested on animals. It is goat milk soap made by Jenness Farm in New Hampshire.
All the soaps are made in their home kitchen using goat milk from their own herd of goats. It started as a 4-H project and has continued to expand. I have to give my complete recommendation to these products, because I have dry, rough skin and when I use this soap my skin is nourished and smoothed noticeably even after one use.
I know it sounds weird, but everyone should try this stuff! There are so many amazing scents to choose from and it would be great to support this small family business from my home state!!!