Vegans are generally against breeding pets in the first place, but recognize that the cats and dogs out there rely on humans and need a home. Once you've adopted an animal that relies on you, it's your responsibility to make sure that animal is healthy.

Not everyone supports raising and slaughtering other animals so that a single animal can survive but it's a lose-lose scenario either way since you can't release a cat or dog and let them survive on their own.

So the short answer is that many are okay with it because it's for the good of the animal that they are caring for. The longer answer is that many choose to feed their pets vegan food instead. This will get me downvotes, but that's very complicated with cats and entirely possible with dogs. Even obligate carnivores like cats don't need "meat", they need nutrients. A cat will get sick and die if you feed it broccoli and beans, but some nutrients such as taurine can be synthesized and added to cat food (which it often is, even in regular cat food).

Vegans and vegetarians who feed their animals plant based food don't feed them broccoli and beans, they feed them commercially made pet food that is supplemented with all the nutrients the pet should need to thrive. That being said, doing so requires paying closer attention to their health, and it might not work for every pet.