shortwave, I tend to agree that putting out a buffet for random critters is unwise. When my wife had barn cats, their food was put up on a rafter, where the cats could get it, but most of the other critters that might be able to get it would have to run the cat gauntlet.
As far as my parents and their neighbors... I guess they don't worry about raccoons and opossums (Florida; they have plenty of both).
With regard to your liability question, what extreme would you like to use? Should a person who puts out a bird feeder or keeps berry-bearing trees and bushes bear liability for the neighbor's car washing costs? Or should people who put out salt licks for deer be liable for any potential damage done to area crops, by deer transiting to and from the licks?
It's an easy game to play, really, just keep going up a notch.
My basic take on the lot, though, is that animals behave like animals. If you need to control them due to potential harms to your livestock, crops, etc, then so be it. My point is that it is a utilitarian argument, not a moral argument. Some people here are demonizing the critters for acting like critters, as though they need a moral justification. My point is that if they have a real need, they have a real need. If they don't, then it really comes down to they like to shoot stuff because they can.
In which case, they are no different from the cats.
So, people either have a real reason to control the beasts (which they might well have - protection of property, control of disease vectors, defense of locally threatened species could all be valid), or else people, like the cats, like to kill things when they can, in which case their moral arguments seem very hypocritical.
I've known quite a few guys who liked to shoot things because they could. I am not one of those guys, but there are a lot of them out there.