I've worked for three veterinarians in the state of Washington and all three have you sign something before they will perform euthanasia. The form states not only that you want the animal put down, but that you are the legal owner.
I doubt that would be the case in the circumstance you are referring to, so taking a cat to a veterinarian to be put down would involve lying and saying you are the owner, at least in my state. The only time I have seen vets waiver from this were times of extreme pain/suffering, etc., such as people bringing in dying animals who were just hit by cars, etc. Then they can attest that it was in the animals best interest. Maybe someone else could chime in with the repercussions of that type of lie, but I do think that if you killed certain people's cats, they would certainly come after you with whatever legal means they have. Not all cat owners, but some are really extremely attached fanatics.
I'm on the fence on this one, because I own cats that escape from the house, so are indoor-outdoor, but I do care for them very much although I'm not a fanatic. But my cats never ever bother poultry and in fact, catch mice and other small rodents that prey on their feed. The chickens even enjoy the dead mice bodies that the cat drags back to set on my porch. I thought the cat/chicken combination was working excellently at my house and understood why cats survived all these centuries, because their job was protecting the very important grains used to feed the chickens. My chickens even follow my best mouser around when they are free ranging, hoping he is going to provide them with another body (he only catches and kills them, doesn't eat them). If I were raising chicks I would build a protective enclosure for them because I realize the natural order of things is that a cat will only eat prey small enough (unless you kill it for them). It cracks me up when I see venison and beef made into cat food (I'm picturing 20-30 kitties in tandem, working to catch a deer!). I do wonder if my cat would consider quail prey, being smaller.
And even in the city, cats have natural territories. Better to train the local cat that your chickens are off limits than get rid of it/deter it/fence it out than have to train the next one that takes over its territory continually. I find a hose works really well in repelling cats from areas that I don't want them to be in. and I am more often watering as opposed to walking around with my BB gun. I do have one that we use to shoot at coyotes but again, I would rather scare off and train the current predator rather than dispose of this one and have a new tenderfoot move in and investigate the place all over again, although my husband does use the real gun re: the coyotes when he is home. I do understand where both sides of this issue are coming from however and worry about loose neighbor dogs even though I'm a dog lover myself. People just have to act responsibly and since they don't always, you need to build a good enclosure and/or keep a good eye on your own.