I reckon it's all a case of getting a balance - allowing each species its rights whilst bearing in mind how it impinges on another - and taking steps where possible to limit that. Like cleaning up after your dog, or taking steps to prevent your cats messing in other people's gardens. Yes, it's impossible to stop them wandering, but if they're trained right from the start that they can't go out after dusk (which is the riskiest time for bird-catching), they may (allowing for exceptions) get used to the routine of only going out during the day.
My cats vary in habit - and appearance - you wouldn't think they were siblings. Jess the tom always showed an interest in going out, Pixie his sister is a homebody. They were house cats for 4 years as we were in a flat, planning to move, and I didn't want them to get used to their territory if we were due to move to a different one. However, Jess tended to bolt outside whenever he got the chance. Our new house has a cat flap, which I lock at dusk and open after breakfast. Both cats seem content with this. Jess likes going out but doesn't wander far because he's had several run-ins with an aggressive mog who's literally thrown himself at the back door to try to get at Jess (for a boy, he's very placid and never hisses or scratches). I have been known to chase this cat up the garden in my dressing gown, wielding the potato peeler that was in my hand when he attacked Jess and screaming 'I'll swing for you!!!' Hope none of you are my neighbours !
Pixie likes to go out when I'm out, but views the flap dubiously and prefers to have the door opened for her - pity she hasn't met the bully - she scratches and hisses with a vengeance!
As for the birds, maybe it's because they've been house cats and therefore voyeaurs most of their lives, but mine sit and watch birds walking about on the grass or using the feeder, but I've never seen them try to stalk one. The only thing they've ever caught was a mouse back in our old flat. Or maybe it's because they don't get to go out at dusk. Either way, I seem to be able to run a bird-friendly garden and have my cats. I just wish it wasn't such a cat friendly garden for the neighbours! The good thing about all this rain is that there are fewer cats about. Otherwise they've loved all the freshly turned soil from my gardening efforts and nearly killed on of my newly planted bleeding hearts.
I shall try one of those sonic things when I can. Do they cover the whole garden or do you have to direct them at one spot?
As I mentioned earlier, the bottles of water don't work (my cats like admiring their reflections!!) and our garden's too small to leave a dedicated poo plot (only 25 x 50 foot long, so all space is precious planting ground)