I just ran across a promising resource: soapnaturally.org. The site is mainly for soapmakers, but there is a page with links to people who make traditional soaps around the world.
I have not been able to check all of them out – sometimes people claim to be traditional soapmakers, but they use raw materials that contain detergents (even SLS), so it’s important to check first. The sites I checked clearly described the soapmaking process on their sites, so they are true soap makers. (I have not used any of these products.)