Most states allow farmers and livestock producers to protect their crops and animals but they don't necessarily allow wholesale killing. Take my native CO for example: livestock producers can shoot coyotes all year long because it is classified as a varmint but there is a season on fox. So unless you catch the fox in the act of killing your birds you can't just shoot any old fox if you lose a few. Same with cougar/bear, ranchers can kill a predators that takes cattle but they have to target the guilty animal and they can't just kill any cougar/bear they see. Cougar and bear are both covered by seasons and tags and cannot just be shot on sight if a cow ends up dead.

My take on this is the OP lost a few birds and is willing to kill any fox in the area and that may or may not actually be legal to do. I'm all about protecting livestock but it has to be done in accordance with whatever laws cover the area.