What's "legal" doesn't mean we all have to agree with the ethics and morality of it. People are entitled to their opinion on a public post in an online forum and to respectfully present another point of view. If you do a little research, or have any experience with raising livestock, you would know that when you kill a territorial animal like a bobcat or a fox, another will just move in to occupy that territory. Rarely does it solve the problem, and I doubt it will here if your neighbor isn't securing her chickens. It is not difficult or expensive to build a chicken run and coop that will stop predators from taking your chickens. A never saw a predator show up with wire cutters.
And make sure that enclosure has a barrier running a couple feet into the ground. My buddy had what he thought was a secure enclosure for his ducks but noticed 3 ducks vanished. After searching the enclosure he found a hole that the coyotes dug to drag the ducks out.
Speaking about ethics and morality. It’s all silly when you think about it. We dispatch rats with out a thought but in certain parts of India they are worshipped. We eat pork but did you know a pig can be a pet that is as intelligent and affectionate as a dog? It’s funny how we ignore ethics and morality when it comes to eating animals we’re culturally accustomed to eating(killing).
Within legal limits any animal is game for pesting/depredation IMO