Dogs are still descended from wolves, and wild canids live primarily on meat. It's cruel to get an animal that lives mostly on meat then force an un-natural diet onto it based on your own belief system. Don't want anything to do with meat? Then don't get a dog or a cat. Buy a herbivore for a pet. Look into your dog's mouth and tell me that he's meant to be living on plant matter alone. Their entire physiology demonstrates that they're primarily carnivorous, and omnivorous in practice.
I find it revolting when people force their personal beliefs on their pets. Many cats have died because their idiot owners forced them onto a veg only diet, and while dogs can survive without meat, it's still disgusting to me to do that to an animal for the above reasons. Get a pet rabbit if your principles extend to your pets, don't mistreat a dog for selfish reasons.