Dog owning programmer here. Our dog is a rescue and very anxious when left alone. We go to unreasonable lengths to limit his anxiety.
As an example, we just moved from Vancouver BC to Oslo. There are no direct flights between these two cities. To minimize the shock to our dog, we flew in to Amsterdam and spent two days on the train to get to Oslo. We both whole-heartedly felt it was the right decision every minute of the long journey because neither of us want to see him as distraught as he was that day.
We rescued him within 30 days of me going out on my own to freelance in 2011. Despite many concerted efforts of curbing his separation anxiety, he can't go 30 seconds alone without howling his sadness. Given that, every career decision I've made since has gone through the lens of 'What about Charlie?' I understood what I was in for when we got him, and it has certainly introduced limitations to the work I'm able to pursue, but we wouldn't go back on that initial decision.
I've had long running contracts where he was welcome on site. This was the difference between me being able to take the work and me turning it down.
In my biased opinion, quiet and well behaved dogs can co-exist in a productive office. If a pro-dog policy facilitates talent acquisition, in-person communication, and doesn't disrupt anybody - it's a net positive. If the dog is a misbehaving little brat, that's a different story.