Since they're pets and you don't want to anger your neighbors, you could try a couple different things.
For one, cats don't like the scent of Coleus Canina. It's commonly referred to as the "pee off plant" or the "scaredy cat." The scent bothers cats, dogs, and foxes. It's actually a beautiful plant, too, so planting it in a garden won't be unsightly.
The second is the herb rue, lavendar, or pennyroyal. Again, the scent of the plant should deter the cats. The rue is also a beautiful plant with blue flowers, so it won't be too obvious as to what you're doing.
If you don't mind the cats in general and would be okay with them in one specific area, you could plant a cluster of cat nip in a "cat safe" area. This way, the cats are distracted by a treat and wouldn't be likely to venture into other areas or go after the birds. You could also put a little sand box here which would serve as a litter box. While you'd still have the poop problem, it'd more than likely be contained to one area.
Water is also surprisingly effective at keeping cats out of yards. Most cats, even outdoor cats, prefer not to get wet. I'm assuming the cats are out at certain times that you've noticed. You could try using a sprinkler and setting it for these times so that the cats learn that your yard will giving them a shocking shower. They'll learn pretty quickly that your yard is no longer fun and find another place to go hang out. This has the added benefit of a beautiful lawn.
Also in the line of water, there's a product called Scarecrow Sprinklers. These detect the presence of an intruder and fire off a blast of water at it.
Another product is Shake Away that smells like the urine of cat predators. Because it smells, the cats will learn that this yard has predators and isn't safe.
You could also try blood meal fertilizer or mothballs. I'm not sure how effective they are, but some people say this works. Mothballs are toxic, so they should be used only in a covered jar or tin so that no wildlife can get to them.
Now that I've written a book here, I guess I could stop.
I really hope you find a solution so that both the birds and the cats are safe. I really don't like when cats are left outdoors, not only because they hurt the native populations, but they're not prepared to deal with things like cars. I've seen so many people do awful things to cats because they were a nuisance and it really makes me sad. I don't think you'd do anything to hurt the cats, but your neighbors should be a bit more careful with them!
"Mockingbirds don't do one thing but make music for us to enjoy. They don't do one thing but sing their hearts out for us. That's why it's a sin to kill a mockingbird."
- Harper Lee, To Kill a Mockingbird
