My rule is that as long as they don't bother me and mine, I leave them be. Not every predator will come after your birds. Save your bullets for the ones that do.
My area is chuck full of coyotes. Instead of trying to kill them, I keep my pets and poultry in a secure manner. I haven't had any loses. I don't have coyotes trying to break in, so I leave them alone.
I've got at least one raccoon on this block. He's never shown any interest in the birds, so I don't bother him. If he starts trying to break into the coop, then that changes things. But he hasn't, so I've got no reason to defend myself from him.
The local coyotes do me a service. They eliminate all the stray cats and dogs that have been dumped out here "to go live on a farm" so that I don't have to deal with them. They keep the rodents under control. They get at least a few of the nuisance over-populated deer. And I'm sure they are the reason that there is only one raccoon in the area.
I try not to upset the balance of nature any more than I have to. I'll protect my own, but not until I am provoked into it.