My boyfriend is what most people would call a 'twitcher' (not actually, if you know the real meaning of the word but he is a bit of an obsessed birdwatcher). Is he upset that the stray we just adopted can go out of his catflap anytime he likes and kill birds? No. He more often kills mice, but he has brought in one bird while we've had him. Having said that, the slightly stir-crazy birdwatchers are the only people I've ever found to object to cats being able to hunt in the UK. I think it's an attitude thing - it's also fairly accepted that cats will poop, none of our neighbours have ever minded (they love our cats) and they usually bury it anyway.
It's a bit of a rareity for them to bring in birds, I find. I've had 4 cats not that LOVED being outdoors and provided good weather will spend most of their time out. One didn't really bother hunting. One only ever caught birds but rarely. One was the 'mighty hunter' and didn't go a week without little rodenty 'presents' but NEVER figured out how to catch birds, for all his trying. Newest one has caught one ground-feeding bird.

It's not nice. I don't want mice, birds, or the occasional squirrel (cats aren't supposed to be able to catch squirrels but the last one managed and I'm pretty sure it wasn't road kill the second time...) brought it. I highly doubt it'd decimate any population and frankly, there are so many supposed 'threatended' birds in our area that we're one of the places that balance out low populations elsewhere. So what do we do? A collar with a bell. Now he doesn't catch anything.