In my yard my greyhounds are fine, my yard is small, only muzzles are for those who eat poop . When they used to go out running in a large area, they AWLAYS wore muzzles, no exceptions as did any other dogs greyhounds or not, they wore muzzles too. Greyhounds are taught to chase, they love to chase, they love to run and they are competative by nature AND by training.
I don't do dog parks due to the issue of poop everywhere and worm infested poop, unmuzzled dogs etc. Greyhounds are not the only dogs who can have issues with small dogs.
Muzzles are cheap and honestly I've never had a greyhound who objected to the muzzle for more than a minute or two. When I had fosters coming and going, all dogs wore muzzles in the house for the duration of the foster's stay, I had more than 45 fosters and none of them were bitten or bit my dogs, they wore muzzles.
I still have 2 dogs who have to be muzzled when I leave because they tend to get into stuff they shouldn't if they aren't muzzled. Also I have a 14 year old greyhound and and I worry about them attacking her if she should fall etc. (yep, I know that they can do severe damage with their feet if they wanted to, I pray that they never do)
Bottom line, better to be safe than sorry and also, I can't afford a lot of vet bills to repair injured dogs.