Most people would agree that cats are carnivores, and need meat to survive. Dogs are omnivores. They can survive on a carefully planned, nutritious plant-based diet, though many vegetarians still feed their dogs at least some meat or meat-based dog food. Not that this matters much, but dog food generally has much less meat as a percentage than cat food does. (PS: If you have a dog, and would and would like to find out more about a vegetarian diet for dogs, check out this article, or this one.)
So isn't it hypocritical for someone to not eat meat, while still feeding meat to their pet(s)? This is a dilemma many vegetarians and vegans continue to struggle with, and understandably so. The question itself seems to require a "black or white" answer, but reality can be a lot more gray. I have four cats, and, like I stated above, cats are carnivores, so I do feed them meat-based cat food. I don't like doing this, but it was a choice that I made when I decided to take them in. All of my cats were either saved from shelters, or found sick on the streets. Was it wrong to save the lives of these animals knowing that they would need to consume meat? I personally don't think so. As I have written many times before, I’m not a big fan of the "saint or sinner", "black or white" approach to these issues, but like to see the big picture, - how one lives, what one eats, what one wears, etc. Let's take a couple who eats meat, eats dairy, wears leather, and feeds their dog meat. If they eliminate the first three things from the list, and only feed their dog meat, they will have eliminated 75% of the harm that they do, from the perspective of interacting with other animals. 75% is not 100%, but it's a lot closer to 100% than it is to 0%. At times like this, it's important to be supportive and praise someone for the progress they have made, than to mire them in guilt and call them a hypocrite for what they haven't.
An important thing to remember here is that humans (at least most of us) have a choice when it comes to eating meat or not eating meat. Animals don't have this choice. While we should respect the lives of all sentient beings, we should not mimic the behavior of these animals, such as the carnivorous diet of cats for example. I believe that were given freedom of choice so as to be able to choose a compassionate path, and that, for humans, vegetarianism and especially veganism represent progress.
That said, helping carnivorous animals survive is not a bad thing. Look at the organizations that work so hard to preserve species of birds and wild animals around the world. More often than not, the animals in these refuges require fresh meat for survival. On a more local level, like many people, I care about our shelter pets. I have done what I can to help encourage people to adopt, and to spay and neuter their dogs and cats. Encouraging the spaying and neutering of pets is something that I believe everyone who cares about farm animals should get involved in, since humanely cutting down on the population of unwanted pets will go a long way to minimize the amount of meat that is used to feed these animals, thereby saving many lives.
When all's said and done, it all boils down to how comfortable you are with having a pet that requires meat to survive. Like I said, for people who truly empathize with the plight of all animals, it's often a very hard choice to make. Some vegetarians/vegans will not have pets for this reason alone, and I can respect that. I also respect and understand the other side of the argument, one that recognizes that carnivorous animals sometimes also need to be saved.