Sound advice all round here. I fostered an ex racing Grey a little over a year ago and I managed to get him to leave my cats alone when I was in the room but would never have left them unattended. His forever owner reports though that he is a buggar for chasing local cats.
Most rescues that I know of cat test using various suppporters cats so I would doubt the one from which Hobnobfanatic adopted her Grey is any different tbh. I think that your awful experience, Hobnobfanatic, was probably just plain damn bad luck and you adopted a Grey with an attitude like my ex-foster boy.
To confirm another poster's thoughts, yes, LurcherLink do cat test and if adopting from them of course will ask if you have cats so they can assess the situation accordingly. They are very good and the owner, Kaye, is a very dedicated and helpful lady.
Greys DO have a greater prey drive than most dogs in the main of course but not all are like that - I have had a couple of ex racers in my home from time to time who have been just fine with my cats. As has been said, check, check and check again. Matching the right dog to the right home is an essential part of rescue although I know that there are some out there who aren't as responsible as they should be and some who are over-zealous in their requirements. The answer is to approach a few rescues, not just one, and make an informed decision. Remember too that Greys are so often abandoned that it is not only breed specific rescues who will have them in their kennels, most all-breed rescues will do too.
For possible matches and advice as to where the independent rescues are in your area, your best bet is LurcherLink's forum. Often, when I mention the independent rescue I volunteer for locals say, "Who? Where?" yet it is only a few miles away. There may be one or two out there you have yet to become aware of.
People tend to be unaware too that Greys are lovely, gentle pets and do not require hours of walks a day, far preferring a couple or 3 or shorter chances to run like idiots and then to put their feet up and snooze. You clearly know this, but as a rescue volunteer ay I say - Please spread the word!