karen,
I laud your intentions and the kittens you rescue are much better off than fending for themselves in the wild. BUT, even the most domesticated house cat will catch a bird if it can, it has no choice in the matter, its brain is just wired that way. The only domestic house cats I know that don't bother birds are the ones too old and too fat to catch one. My best friend's cat, Buster, fits this category, but still sits in the window from time to time, imagining he could catch one of the birds outside the window, following their every move intently. One of my wife's best friends has 7 inside cats and 6 outside ones (The outside ones are feral and are kept in a pen with a top, keeping them in. She feeds them and takes care of them, but knows they will not become tame) She would never dream of neutering them and releasing them. Like you, any kittens that result are socialised and given away. I have no problem with this procedure, other than it still resulting in more cats that, depending on their owners, may or may not be allowed to roam free.
BTW, how do you think that cat made it 1,300 miles all the way to Chicago from New Mexico?