Outdoor feral cats are terrible for the environment/local fauna, dogs are domesticated so much that an outdoor feral life is miserable for them. It is absolutely compatible with veganism to give a home and care to cats and dogs who would otherwise be out on the streets. Buying specialty/novelty breeds from a breeder is not.

Veganism is less about absolutes, and more about reducing/not supporting animal harm and suffering wherever possible. Most vegans would agree that taking in a cat or dog and feeding them appropriate (meat) food is better overall then letting them roam feral. It is a very utilitarian view with regard to animals' wellbeing.

Im not vegan but I do have vegan relatives (with cats). Also you don't need to be vegan to agree with the points I brought up in the first paragraph.