Soap itself tastes nothing much at all. And when I say soap I mean the chemical compound you get by heating together some kind of fat (animal or plant based, doesnt matter) and some kind of a base (typically lye but there are other possibilities).
Problem with most commercially available soap bars (and shampoo and dishwashing gels and whatnot) that beyond soap they contain else, such as perfume, things that tastes bad and irritates the skin and mucous membranes and such.
If you can buy home made soaps which contain little to no additives. I bought via webshops but some walk in shops sell em too.
Just with soap like those, one can cover many things. Can wash, shave, clean clothes and dishes, brush teeth. Yes, you can wash your teeth with soap (as noted, it doesn't taste bad) in fact one ingredient of toothpaste is soap! What? What did you expect to be the thing in toothpaste that foams and cleans? They usually don't list it as ingredient, but they do some kind of fat and some kind of base. And that's just soap.