One cannot protect a child from every form of dirt and bacteria out there. When we have tried we have created kids more prone to allergies and super bacteria. As a parent, I would be worried a lot more right now about MRSA than fecal matter. There was an old truism my mother used to say, which I think still holds true, “You eat a peck o’ dirt before you die.”
Further, people with pets are just as entitled to use the parks and beaches as you are. I think special dog beaches and dog parks can be set aside for off-leash activities.
Ever been at a movie or sporting event and seen a parent leave a dirty diaper right there among the seats? Euwwww!
Gone to a bathroom where someone tinkled on the seat because they would put their precious germ-free a** on it, but could not be bothered to wipe off their piss so the next person had a clean seat?
I hardly think dogs are the big issue in terms of health and safety as long as ordinary precautions are used.