While cats are native in some places, evolutionary mechanisms stop working when a predator has an unlimited supply of food supplied by humans. The problem of cats nowadays isn't their existence, but that the amount of cats per square meter is more than the ecosystem can support. Usually this would easily balance out by the predator dying. But with humans feeding cats, they can rampage the ecosystem until it's destroyed without checks and balances. Feeding a predator and letting it outside is never suitable.