I think it really changes depending on the bird and need. Like in the states we have a bird called a Grackle that is a much of a problem here as the Rabbit as been for Australia. It's not a native bird and was released by people who wanted The Birds of William Shakespeare' here in North America.
They don't belong here, have reproduced like crazy, are obnoxiously noisy, mess up things and have severely damaged many native bird populations. About a decade ago some company started shooting the ones on a golf course and a bunch of people started protesting and shut them down. It's not just about the grackle, but also some of the native birds are needed to help distribute seeds in the forest. With out those trees being spread, animals can't live there that need them, animals too start dying out ect., etc. It's a complex ecosystem and those birds are messing it up. So I'm ok with removing them.
Or some people eat them. But just to kill something that advanced for fun? That's rather messed up.