I am not fond of dogs. In fact, I do not like animals very much in general. However, regardless of whether one likes dogs, I think we all agree that dog excrement is not very nice at all.
Compare dog dirt to sheep excrement. It is quite different. Sheep excrement is a bit messy, but not much more than mud. It dries out easily in hot weather. The smell of sheep excrement is not that unpleasent, it is part of the English pastoral experience. The reason for the difference is that sheep only eat grass, while dogs eat meat. Hence, dog dirt is a serious potential health hazard. Being exposed to dog dirt is not very good for you at all.
Most places have laws to stop dog fouling, however, there are people who are careless enougth to let their dogs foul up. There are also stray dogs.
You may think that you are careful enougth to avoid stepping in the stuff. However, it is very messy. Even after the bulk of it has been washed away or consumed by insects, there will still be traces of it that you would never notice.
For the sake of your children, take off your shoes at the door and ask visitors to remove their shoes. Even if you do not have children and do not care about your own health, ask visitors to remove their shoes. That way, other people will feel more comfortable making their own homes shoe-free.