Supermarket shelves are dominated by two kinds of butter: conventional dairy-based butter or plant-based vegan butter made from palm oil. Vegan butters are more sustainable than dairy butter, but ideally should be palm-oil free. I found two that I like.
So, depending on your priorities, you may want to find soap from a company that doesn’t test on animals and contains simple plant-based ingredients. Soap made from animal fat will have the largest carbon footprint