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.
To be fair i frequently consider the ethics of owning pets.
I am not vegan and have multiple pets. There has only be a short section of my life i lived without.
I don't think i could personally choose to own a dog, though i love the one my partner came with and have fond memories of those from my youth.
its just how restrictive their freedoms are. Almost always in a closed area or on a leash. It’s a conscious adult animal who are we to say its wrong for it to act on its instincts. They cant leave or complain much, Its practically enslavement.
Cats however can roam freely and it’s not uncommon here for cats to visit multiple homes, possible finding a different house to live. Cats only listen if they want to and instinctively act with no regard of your human ideal.
So i see much less issue there having them a part of a family.
Now before every online wildlife enthusiast screams at me for not oppressing their roaming space. Wild cats are native where i live.. locking them in is locally considered very cruel.
The fact we have to discuss that is an argument for just not owning any pets though.
A friend had a cat move in voluntarily, so guess that would be one way. It's still an outdoor cat and can come and go as it pleases, it just seems to prefer staying there. It just gets food, scratches, and a place to stay, but is technically pretty much a wild animal. It behaves as if its lived with them for its whole life and tends to sleep next to my friend in her bed at night.
It's not vegan, that's all there is to it. Some keep animal companions since it's less harmful for them than a shelter but considering them "owned" is treating animals like property which is not vegan.
If you let a cat outside and they come back, that would be the closest you could get to an animal consenting, without actually talking to them. Also dogs naturally drifted to humans, so dogs chillling with humans is kind of their natural behaviour? The rest would be harder to justify.