It sounds like there are two different things here.
DOS, which is the oxidation of oils and has nothing to do with bacteria and perserviatives (Adding antioxidants can reduce this),
and bacterial/fungal growth which is what you would need a preservative for.
My husband is a microbiologist and we have had several discussions about bacterial/fungal growth in soap.
Our general consensus was that in the soap it's self, like Lindy said, there may be water around (like when the soap gets used), but the water MAY not be available for bacterial growth - like when it snows and the plants cannot use the water because it is not available, it is frozen and the ground is dry. But of course it is not sterile so there is likely always small numbers of bacteria that can live in the conditions of the soap, but there is probably competition with other bacteria for the limited amounts of usable resources, as well as less than optimal conditions for extreme bacterial growth (to the point where it would decay), and conditions that can change frequently when in use.
We think that it would be more likely for a fungi or mold to grow on the soap's organic bits, and be more noticeable than bacterial growth, as a fungal hyphea can usually be seen with the eye compared to a bacteria. But even if these things are present they are not always visible. Probably because the soap is being used to frequently and they are getting washed and disturbed, or drying out, or the conditions are always changing and it cannot survive for long enough to grow to a visible size.
There are just so many factors, and they often change.
Personally we have never had visible growth on our oat soaps or soaps with plant materials in them - HP soap with oats and plant stuff added after cook. I have heard of people with fresh flower petals on top of molding in the packaging, but that would happen regardless of the soap factor, and it is likely that the environment was consistently moist with available water (non soapy) from condensation on the wrapper and in a consistent temperature, most likely warm room temperature.
And if the soap is dry, bacterial and fungal growth is very unlikely as of course most bacteria and fungi need water to grow. Even if they are present, they don't have the resources to grow up to a noticeable amount.
But these are all just theories based on our observations of our soaps (including oat soaps), observations of how other micro organisms grow from Michael's work, and we had to assume the micro-conditions of the soap as we don't really have any way of actually testing the amount of available water or micro-nutrients in the soap.
But anyway, these are just theories and ideas and stuff that we have been thinking about