I would probably get all kinds of diseases if I sniffed every bare asshole from every mammal I meet, humans included. I’d definitely get sick if I sniffed a dozen random turds a day. But dogs can do it without any apparent issues. Not only that, but they can do it across different species of animal, too.
What dark arts are afoot within the beak of the dog?
Luckily, there’s really not many pathogens that cross from poop to the airway.
Then, the sinuses and the mucous orifices produced there are part of our immune systems, as well as dogs’.
From there, the lungs have a similar level of defense, so the chances of sniffing a bunghole resulting in a disease are extremely low.
Even with direct nose-to-anus contact, there’s very low risk. The stuff that grows well in the colon and poop just aren’t evolved to set up shop at the other end, and vice versa.