It's a tough question.....since a cat's natural instinct is to pounce on a bird.  But wild birds will fly away.....I would not leave a cat enclosed in an area with birds or chickens that can not escape.

Thanks for repliess to my post. 

Cats are very important in the South to control rodents like rats.  You may feel sympathy for rats, but I do not.  I think rats are an invasive species too.  Rats also kill birds.  I have to consider this factor as well as the ones your posts mentioned.

As to chickens being hunted by cats:  an adult rooster can "take on" a cat.  Dogs are a problem in that regard:  two dogs got into my yard last year and killed one of my roosters.  The rooster was defending a hen who was on a nest.  The hen is still OK to this day. 

I reported to the police that the dogs had killed my rooster.  The cops failed to do their job, as usual.  The local cops did not call the dog pound.  One of them placed one of the dogs in the yard next to mine.  I called the cops on other occasions when I saw the dogs roaming the area.  They failed to call the dog pound every time.  Police corruption is rampant. 

Again, thank you for replies to my post.

Tell the "myth" about outdoor cats to all the dead doves and bluejays I find in my yard.  The birds hardly come to my feeder anymore because I have neighbors that don't keep their cats indoors.  Plus my driveway and yard always smell of cat urine.  Gross.