I'm very dubious, nay, scathing on this labelling of a species as bad "they kill songbirds" and hence "bad". There have always been magpies and songbirds and each has to make a living. Magpies doubtless take chicks of other birds, but songbirds eat worms etc.There is a balance and all seem to do OK, Environmental change is what really hurts species not the ongoing cycle of predator and prey
Pigeons are "bad" because they are sucessfull yet doves are "good" and represent peace.
OK I don't want rats in the house but outdoor rats -live and let live.
We have a cat and she happily hunts birds and rodents as its her nature, and to be fair she eats them mostly, but the garden is full of birds and I have yet to hear of a shortage of rats, however many dead ones she brings in
Back on topic in another life our timid scardey cat maine coon was in the garden growling one day with the other 3 cats looking on from a distance. He proudly munched his way through a whole magpie, bones, feathers, the lot, leaving only a pair of feet. His bigger stronger bolder brother caught nowt as he had the stealth of a herd of hippos.