Probably the most wide-reaching thing to do is awareness education.
My experience with rabbits in and around my garden tells me there's only so much one person can do with a rifle and road kill.
Cat owners especially, since that's the source of the cats! Whether allowed to roam freely outdoors, or not protected from "escape" from the home, or just "released" due to behavioral problems, or changes in their humans' living/financial situations.
Would-be cat owners about their options for adoption of stray/feral cats (versus 'breeders' and pet stores), and responsibilities of cat ownership regarding wildlife.
Bird-lovers and birdwatchers, many of whom are already likely to be aware. There may be good bird friendly practices for siting birdfeeders to provide cover for birds, safe perches, no/poor access for cats to feeding sites. Birders might also be good allies in effecting legislative change, regarding cat policy for housecats and feral cats, funding for bird research or feral cat capture, creating sanctuaries.
Lawmakers who could pass some beneficial legislation, whether restricting cats (microchips and licenses, ban on outdoor cats? leash laws? fines?), protecting wild birds, limiting habitat loss/degradation, etc.