Why are stone ware and dutch oven items exempt from bacteria?
I'm not sure what you mean by a "stoneware pan" in this case...but some pottery used for cooking shouldn't be washed with soap.

If it's glazed, then you should certainly clean it with soap, there's no reason not to.

If it's unglazed, and it's really stoneware, it should be safe to wash it with soap; since stoneware is watertight, the soap will stay on the surface, and you'll be able to rinse it off, so using soap is fine.

For water-permeable baking stones, like a pizza baking stone, or some domes used for baking bread with a french-style crisp steamed crust, then using soap is a bad idea, because you typically can't rinse the soap out afterwards. I've never tried washing one with soap, but the instructions that came with my pizza baking stone say that a soapy pizza baking stone is ruined and unusable for food.

For unglazed earthenware used for pizza, bread, or similar, you clean it with water and/or heat: if it gets dirty with something you can't wash off without soap, the remaining option is to burn it off by heating it to a high temperature in the oven, and then brushing or rinsing off the ash. This removes the "food" from derobert's list of things needed for bacteria to grow, by turing it into less nutritious ash.