During the American prohibition of alcohol, many breweries turned to soap manufacture because the facilities and tools used were the same.
Interesting. Does that just mean they both boiled stuff in big vats, or was the similarity deeper than that?
I've made beer, and know how to make soap (but a sudden stint of unemployment stemmed the money for that sort of hobby). It's logistically similar, yeah.
To make beer you add ingredients, thoroughly stir a solution, pasteurize (heat) it, add an organism that initiates a transformation, then sit and wait.
To make soap, you mix up a solution, thoroughly stir it together, then sit and wait as the reagent you add (lye) saponifies and stiffens the solution. Heating it carefully is also usually involved.
Really the only specialized tool involved at all is the molds for blocks of soap... at least given the methods of DF's time period. Everything else involved is a fairly flexible tool that can be used for either role just as effectively. The process gets even more similar with castile soap (made from oils like palm and olive oil), as opposed to sodium tallowate soap like the dwarves make.
Dwarves are probably using nothing more than a cauldron and a big wooden paddle to brew things, which is exactly what they'd use for large amounts of soap.