> Whereas other wild species who espouse pretty much the same behavior - rats, foxes, mice - are seen as pests.

I have not heard of anyone having a problem with rats and mice hunting other animals. They are mainly considered pests because they eat human food stores. And the only context I have heard of foxes considered pests is when they hunt livestock, chickens, geese etc. If a domestic cat starts hunting chickens, I am pretty sure it will have consequences as well.