I mean, if a household that keeps kosher has two sets of everything (plateware, silverware, sinks, etc) to make sure meat doesn’t touch dairy…the logic states you should have a different machine/method for excrement-related things to ensure it doesn’t touch your normal plateware and silverware.

I, personally, would not be comfortable using the machine again for food related things if I found out my housemate had washed the toilet brush in our dishwasher. Poop is meant to be expelled from your body, not consumed in any way - may I remind (the royal) you how pink eye originates?