The dogs that come into the office are all well-behaved. It's part of policy, and coworkers aren't jerks. It's still an office, and there's no better way to turn coworkers against you than bringing in a disruptive dog. People are smart enough to know not to bring in a dog that will make enemies.

I like the dog policy, because every so often I have the nice surprise of being able to pet a fluffy dog, at work. In practice it's not so bad as what you're thinking it might devolve into.