I bring soap-- but it is repackaged Dr. Bonners and I have used it for all of my cleaning/sanitizing needs. It is mainly used on me for longer trips.

However, I do not use it for washing the dishes because, well I have no dishes. I use my pot to boil water in and then I pour it into a freezer bag+cozy and let it hydrate. The pot has only boiled water and I don't wash the freezer bag. My spork I just lick clean--- I can hear some of you cringe.