There are obviously many different flavors of vegans, each stopping at different points when it comes to what they consider animal suffering. There are vegans with pets, but they might not agree with the idea that all forms of keeping animals is considered suffering. Other vegans won't keep pets, I'm one of them, because I agree completely with the post you commented on and draw the same conclusion as you that it's incompatible with my beliefs.

There's a middle ground as well, exemplified by Gary Francione (https://en.wikipedia.org/wiki/Gary_L._Francione). He's an animal rights abolitionist, meaning that we should just improve the welfare of animals in the animal industry, but abolish it completely. Yet he keeps pets, by only taking in rescued animals from shelters. He argues that their lives are already ongoing, and we should make the best situation we can for them. But we shouldn't buy animals from breeders, because then we help perpetuate the situation.

I think it's a sympathetic position to take, so yes, it's possible to want to stop people from breeding pets while still caring for the ones that are already here.