Michelle I can understand why you are confused, there are some articles out there that suggest ALL greyhounds can be trained to live with cats and a lot of material that would suggest that a sighthound can never live safely with cats.....
I think the absolute bottom line is that nobody can ever guarantee that your cat will be safe with ANY dog be it sighthound or otherwise, the issue with sighthounds over other breeds of dogs is that they will chase and because of their speed (and their very fast acceleration from a 'resting' position) they will catch 'prey'.
A good rescue, like Gap ;D, will do very thorough assessments and if a dog has been fostered with cats then that is the best situation from which to adopt, BUT even then you have to carefully introduce the two.
You also have to consider the character of your own cat, is it likely to stand its ground or flee? And consider your own character, whether you have the patience, time and confidence to work with your cat and dog to make it work.
We have two cats, adopted as adults together from Battersea. Although when we adopted them some four years ago we were not planning on having a dog we did choose them because they had apparently lived with a dog at some time in their past. One is very nervous, one is quite brave and inquisitive.
We adopted our first GH, Jazz, 18 months ago on the basis that he had lived with cats and was 'cat friendly'. Jazz was a very very nervous and shy dog and to be honest he was terrified of the cats, looked away when they entered the room, really never showed any interest in them at all BUT he would chase them in the garden (they always jumped up the trees or fence when that happened, me heart in mouth berating OH that he let the dog out off lead with the cats outdoors, OH telling me it was fine and he would never harm them....he never did but that was so not the point!)
Our second GH is Dickie, here since June. He was 'cat tested' on the basis of being introduced briefly to a cat that was dog savvy and showed no interest. Dickie is a very 'people' dog, just adores attention so when he came to live with us, while he showed some interest in the cats he reacted with complete submission when we told him 'no'. Because the cats had lived with Jazz who showed no interest in them they were quite 'forward' with him. Again he will however chase them in the garden. I do completely trust Dickie though ever since we took him with us to a friend's house where they have three female GH's and a cat. While their own cat was safely tucked up inside the house while we were all out in their huge garden, the neighbour's tiny, but immensely brave (or stupid?) cat kept coming over the fence into the garden

Dickie ran up to him, then just stopped and smelt him, but boy did I have my heart in my mouth because although they might learn to live with cats you do not necessarily expect them to be 'safe' with 'other' cats....
Finally our most recent GH is a little bitch, Cybil, and I would say out of the three she is the one that we have had to work with the hardest on cat introduction and you would think she would be the easiest being only two years old and unlike Jazz (who was 7) and Dickie (who was 5) to train because unlike the dogs she has not raced but was schooled to race and she has been much more interested. As with Dickie, she was just 'cat tested' ie introduced to a dog savvy cat. We have had to keep her muzzled much longer than we did the boys...while she was quiet and reserved when she first came here she has become much more 'confident' and we have really had to be more cautious with her.
At the end of the day it is not an easy process, learning to trust a dog with your cat, while simultaneously you are attempting to gain the trust of a dog that may already be advanced in years and know very little about life, I often think that greyhounds are big puppies in big dog bodies. I am always a bundle of nerves letting the dogs out of their muzzles and off lead in the house for the first time with the cats and I actually could not cope with that on my own, I have a very confident OH and we deal with it together.
I could not ever live with myself if I put my cats in danger or even if they left home because they were unhappy

You should NEVER feel pressured into taking a dog, it should be the right dog for your personal circumstances and if you are homing a dog with an existing cat I think you need firstly to have very good information/knowledge of the dog you are homing and secondly confidence in yourself to deal with the introductions particularly if you are unfamiliar with sighthounds

Sam x
Bev did an excellent video diary showing Striker's cat introduction