I've only ever had one that killed mice so they are by no means ALL rodent killers. The rest of the flock would happily steal anything she caught and eat it, but she was the only one who ever caught and killed them. The rest shared their feeder with the mice as though they were pets.
I am planning to build a treadle feeder, to eliminate the ability of mice to steal my food in the future.
I have lots of chipmunks. The black snakes keep them under control. They also keep check on the rabbits. Both were a problem until the snakes moved in out front.
In your case, tighter wire and better location for the feed might be the answer.