I think you're wrong to say that people shouldn't use soap. Yes, oils are used in the manufacturing process but the chemical reactions change the oils into surfactants rendering oils water soluble. The whole reason for existence of soap is to make oils water-soluble.
People with sebhhoeric dermititis absolutely should use soap to remove their body's natural oil (which the yeast feeds on) and if they feel the need to moisturise they should use something like MCT oil whose hydrocarbon chains are too short for the yeast to metabolise (as opposed to most moisturisers which contain oils that the yeast can metabolise).