I try to kill kill nothing that I won't eat.
However, I will eliminate things that cause me problems.
If a chicken hawk is getting my chickens, it is history. Chicken hawks are federally protected and I have no chickens. BUT....
If a beaver cuts my trees or messes with my dam, I'm going to use extreme prejudice.
If a neighbors dog starts hanging around my deer feeder or running my cows, it has had it.
Rattlesnakes are safe in the woods or pasture but not at the house or around the barns.
Coyotes kill fawns. However, deer need coyotes just like bluegills need bass to keep them from over populating. I've seen starving deer and DO crashes.
I'm not mad at coons, possums, skunks, foxes, or bobcats. They are all safe with me.
The jury is out on feral hogs. So far they haven't caused a problem.