I do have a quick check in our garden for 'what is the dratted saluki shouting at now' and give the squirrels a heads up before I open the door (not that she stands a chance there, they can levitate)...
Recently theres been a dimwit cat out there, he or she has had a saluki up the bum a couple of times and hasn't been seen since, so hopefully has learned to stay out (my garden is very tempting as we have bird feeders and a lot of squirrel/bird activity).
That is as far as I am going though, cat proofing the yard would mean any cat that DID get in would find it far harder to get out - cat proofing methods are designed to stop exit, not prevent entry (to prevent entry I'd need to put an outward overhang with rollers on the leading edge. I can't legally do that, I'd be encroaching on other peoples space).
Supervising them out there is impractical, a quick check about is fine, and they're not out there if we are upstairs, but thats it, more than that would be unreasonable!
As for prey drive = danger to all life, how ridiculous! Tell me you know nothing about dogs without...
Prey drive is usually pretty specific - the saluki will absolutely go for furry stuff, rats, cats, rabbits, hare - she is an accomplished ratter. She dislikes pigeons but that is more of a hobby, faced with a non-flying pigeon, she just shouted at it from a safe distance (least it explode, I dunno!).
Birds of prey are to be gazed at in admiration and presumably, ancestral memory of following hawks to quarry.
Any other bird life is to be ignored as it is Rude and Outrageous and best pretend it doesn't exist (in the manner of an extremely snobbish member of royalty, pretending the serfs and rabble aren't there). She can stand two feet from the window bird feeder and ignore sparrows, robins, blue tits etc completely.
There is a reason for this - dogs bred to hunt like sighthounds learn very quickly not to waste their time, in fact it is instinctive, on quarry that is of no use to them, that they can't catch or no one wants them to catch.