I have never heard of tooth soap ~ I learn something new all the time on this forum
My personal experience started with a nasty rash around my mouth that turned out was a reaction to fluoride so instead of trying to find toothpaste without fluoride, I make my own "toothpaste" using coconut oil, a little baking soda, a little activated charcoal, a little bit of each of the clays (Bentonite, French green and Kaolin). I also add a few drops each of peppermint and clove EOs. And that's it. I don't add sweetener because it's not supposed to taste good, it's supposed to clean your teeth. My mixture tastes like slightly salty coconut oil with a hint of the clays. I brush my teeth and tongue and my teeth feel smooth and clean and my breath is clean ~ no, not minty fresh like commercial products, that's all from artificial flavoring which is not needed to clean your teeth. I also don't need bubbles in my mouth to know they are getting clean. I really wanted to do tooth powder followed by oil pulling but I just couldn't hold that coconut oil in my mouth long enough
so I just mixed the coconut oil into my tooth powder and that works for me
I can't brag on my oral health since I come from a family with weak enamel and have lost a few teeth over the years due to no insurance and extractions were the cheapest way to go, but currently, since using my current regimen, my teeth have not worsened in almost 10 years, only had to have one tooth extracted due to it breaking in half down to the root, and considering my tea addiction, the staining has lightened considerably. So I consider that a win for me ~ oh! And no more mouth rash!