Your dogs sound wonderful MrsJones, and I like greyhounds and all pointy dogs too, but I think it's fair to say there are some issues with them. Some (not all but a definite number, I'd go so far as to say the majority) of hound-type dog do have a higher prey drive (its generic), particularly compared to say a toy breed that has been bred over many generations to prefer to be close to its owner and stay still. And the ones bred and trained to race/work probably more so than average as obviously the successful racing dogs which are chosen to breed from really, really want to catch that rabbit 
naturally and then than inclination is reinforced deliberately via training. They're not to know that what they've been encouraged to do all their lives is suddenly undesirable just because they are in a new environment. A lot of the ex-racers I know can't safely be walked off lead unless in an enclosed area as their recall is just too bad and small furries would not be safe around them. That's not to say that's necessarily an enormous issue, they are not massively high energy dogs so an on-walk lead and chance to zoom around an enclosed garden is fine for many but if the family have a vision of lovely long off-lead walks in the country park or playing frisbee on the grass, they should know it might not happen with a greyhound (most I know are also bemused by any kind of fetch game but maybe they're just dim ).
Also, lovely that yours are good around cats but most hounds I know are very much not unless they've been brought up around them, which again is very much not the norm for rescue ex-racers. Some, but not all ex-racers have lived in kennels the majority of their lives, which is not to say they've been mistreated per se, they're working animals and often well cared for within that context but expecting them to simply transition problem-free into a busy family home with noises, children, other pets and to be taken for walks with other, potentially reactive dogs around, well, you can see that problems could occur particularly with a novice owner that maybe doesn't have loads of time for retraining and just wants a dog to slot in (again, no judgement here, that's the simple reality for a lot of people that post here or in the dog house board looking for a family pet)...
That being said a lot of the ex-racer charities do brilliant work fostering their dogs out so that transition period is managed by someone experienced and dedicated and they will be able to match dogs with suitable homes so e.g. they can cat test and tell you which ones absolutely couldn't live with one, which ones are good with children, which ones can go off-lead etc. But then again this does mean if you are a family with a cat and toddlers and only want a dog with good recall, no separation anxiety and 100% around other dogs, you might need to wait longer than if you can cope with more behavioural issues. That's true of all rescues of course so not saying people shouldn't do it, I think the 'beef' people have on this thread is that sometimes people suggest an ex-racer as the easy way around this as though they're all ready-made perfect family dogs available for the asking, if that was true I think people would be biting the rescues hands off for them which we know not to be the case...