Often pet microbes are transient (so they just pass through your system) but there are quite a few that aren’t - such as with some of the common bugs listed in that paper (such as H Pylori, which is a class 1 carcinogen).
This is why I think it’s important to make sure our pets diets are just as healthy (and species appropriate) as our own - if we have unhealthy pets in the family they will harbour bad microbes, and keep infecting us (and vice versa if we’re not healthy).