Greyhounds have never met other breeds of dogs while they are racing. They have always been surrounded by other Greyhounds, and at first they may not realize that non-Greyhounds are also dogs. Most do fine after they are introduced and they are successfully adopted into homes with other breeds.
Some Greyhounds are not good with other breeds, especially if they are small and furry. These Greyhounds would need to be in a Greyhound-only home or be the only dog.