We free range so have problems with predators on a regular basis including cats.
I find a BB gun to be effective on cats, it doesn't kill them (usually) and doesn't damage/kill like a stone or a 22 ball bearing from a slingshot. It doesn't stop them coming back though. They take time to learn that if they come here they'll get 'pinged'. They do eventually learn. Gun ownership and discharging firearms in these parts has virtually no restrictions. We do have other, more fatal, options available to us but pinging with a BB or slingshot for dogs and cats can often teach them to keep away - persistant offenders who do not respond don't get another chance to learn.
As for shooting someones beloved pet then I'm afraid my view is that if their owners really worried about them that much then they'd keep them in their own property. We have the same rule for our chickens, if they cross the boundary fence they are fair game for anything that wants to get them. We never shoot any weapons 'over the fence'. If a dog is walking along the other side of the fence, in clear view and an easy shot we don't take the shot, no matter how tempting it is - why? because it's not on our property. If it comes through the fence it gets shot - it's that simple.
We keep our chickens in and around the coop at night, we lose some to dogs, cats and natural predators. It's a fact of life, but we don't allow our chickens to become a free meal for any predators that feel like it. Wild predators usually get softer treatment than domesticated ones, after all it's their job to survive and no-one is looking after them and training them to stay within their boundaries.