Well, I come from both sides of this. When we moved to a semi rural area, I had two foster dogs playing with me outside that saw a squirrel and took off. Before I could find them, the neighbor was saying one killed a chicken. I felt terrible and offered to pay for it. We have AG property but never dreamed people would have chickens on a 3 acre parcel. That dog has been adopted, so no more issues. My personal dogs are poultry friendly.
Now I have ducks out daily in walk in chicken tractors. I surround them with electric netting and have never had a problem. I know the flapping makes most animals go crazy, so I take the responsibility for their lives. I know it's possible to keep them safe. There will always be predators and poultry is simply "The Old Country Buffet" to any predator. I'm not shooting ANY animal for doing what it does naturally, because I didn't protect my poultry. And I'd sue anybody who shot a dog that had simply escaped. I have my dogs penned or with me. If the owner was a chronic offender, I'd simply re-home the dog to a responsible person. There are new laws regarding shooting dogs and animal cruelty is a federal offense now. The days are over for "shoot first and ask questions later" IMHO
It doesn't matter if it's a dog, fox, or bear. Our poultry is always going to feed them, till we stop blaming them, and make a predator proof coop and run. I built our night coop in the barn inside a Ft. Knox predator proofed stall, lined with 1/2" welded wire, with 1/4" welded wire inside that. It was finished when we got a camera with motion sensor for the barn isle.
Every day on this site I see people who refuse to adequately protect their birds complaining that a predator got them. I don't recall ever seeing one person with electric (that actually had the electric ON) say that their coop had been breached. Why does anyone have the right to kill a predator when they haven't adequately protected their flock? Electric wire isn't expensive and chargers can be found used too. Prevention is the best protection, not shooting a person's dog IMHO And being sued is a very real consequence of shooting another neighbor's dog. There have been people KILLED over shooting a neighbor's dog, so this might be the easy way to learn it.