I was doing research for an article I was writing a few months ago and found this particularly interesting academic paper - on contractable bacteria and diseases easily acquired from pets, specifically dogs. It talks not only about being diligent in cleaning up after them but also, in washing your hands, cleaning surfaces, etc.
I was unlucky enough to pick up such a bacteria that now lives permanently in the base of my lungs. I have always been a healthy, fit person and particularly obsessed with cleanliness.
.This took me by surprise and when I asked the doctor how I might have contracted such bacteria, he said you would be surprised as to how many people we see each week with such related illnesses.
I am not saying people should give up the idea of owning a dog or a cat. However, I don't think one should ever become complacent about cleanliness. It might seem trivial, but if one is not careful or one does not teach young children about appropriate hygiene while caring for or handling animals, they could pay a very big price of being permanently at risk for not only these diseases, but a whole host of others - like leading to limb amputations
You can learn more at: One Health Fact Sheet
Resource and Research papers