Headline is a lie: as we finally find out halfway through the article, it's not soap but lye, sodium hydroxide. The solvent is the fairly nontoxic dimethyl sulfoxide, so both of these are safe to release into the environment. In https://news.ycombinator.com/item?id=32515659 sbierwagen reports that the reaction requires 120-degree temperatures so this isn't suitable for in-situ remediation.