Rabbit and other rodents around here keep our bobcats pretty healthy as long as a human doesn't see them, and many of us like them for their hunting ways. I keep my chickens well penned. Coyotes eat housecats and small dogs regularly, but also tend to the rabbit population, and I've got a red tailed hawk living nearby, I think the cooper's hawk is nesting in one of my trees. Like I said, I keep my chickens well penned and provide cover when I free range them. That should be small range really.
for all Texans do plenty of shooting, as long as the coyotes stay off our front porches and outside our fences most people recognize them as beneficial. Animal control says we have bobcats out here, but I have never seen one. They could maybe account for a missing cat or 2.