Best estimate I can find is a medium dog creates an annual carbon footprint about 0.75 of that of an average ICE family car. A large breed might approach that of a big (and in most cases completely unnecessary) SUV.
It’s not just ‘working’ dogs though. Offset that environmental cost (relatively simple to mitigate to some extent – fish or vegetable based food, composting shit bags, no plastic toys, etc.) against the mental health benefits born of the unique relationship between dog and humanity. If someone doesn’t get that, or doesn’t like dogs, then that’s their loss.
On a selfish level, we have no kids. There’s your carbon offset for our dog right there and then some.