They make first contact and the Wolves are appalled to learn about the Dogs, and how they are living in "slavery" and don't understand that the Dogs aren't interested in being "liberated".
That's funny, because I'm a "wolf" and I can understand this. You're selling the capacity for understanding of the undomesticated humans short here. Sure, living as a dog would be my personal hell, but I know it's not their personal hell. Getting off as a dog is pretty lucky.
If the dogs don't understand, we just need to sit them down and give a short history lesson and answer their questions.
"Owning humans? What's so bad about that?" "Let me tell you about the worst triangle in human history and the years of pain and suffering it caused. We're still experiencing negative side effects of that whole ordeal to this day."
"What do you have against selective breeding? It's made us faster, stronger, and smarter!" "Let me tell you about the 1940's and some of the ideas that circulated during that time. I have some photographs I want you to look at. Some journal entries I want you to read. Some documentaries I want you to watch."
And after they are sufficiently horrified they can understand our strong gut response to what they are and what they represent. They will be scared of us and scared of themselves. Scared at what they may do if let off their leash. Scared at their capacity for pure, unadulterated evil and probably ashamed at how their good life far away represents the worst kind of human suffering on this planet.
And after that we can explain what them coming here has done. They've put fuel to the fire. The Eugenicists will come out of the cracks and say "Look at what selective breeding has done for the human race! We have that proof you asked us for right here!". The Slavers will say "See! Slavery doesn't have to be bad. We were too quick to abolish it when the slaves could have been more happy and content than the average man!" Everything that we had worked so hard to build would crack. Oh, you could poke holes in every argument they make but they wouldn't listen. The fact that the selectively bred "slaves" are happy would be all they focused on. And inevitably more people would agree with them. After all the dogs are happy, aren't they? I would be a dog if I could! Have everything provided for me. And if humanity is really this better off if only certain people breed then maybe it's for the best.
Our last resort would be to "free" the dogs. Lie. Say that no, their situation isn't actually good. They are suffering under the surface and that we can under no circumstances tolerate anything that resembles slavery or eugenics. If it's shown to be successful then humans will inevitably try to replicate it, and we'll be back to square one. We'll relive a nightmare. Fight war we already fought only with more deadly weapons. Instead we have to say that no, it's not successful. Even if it is we have to say it isn't because we can't have humans going back to it.
Sure. I could understand why dogs would be happy. However I don't see how they couldn't understand why we aren't fine with them and their position, and why we want to free them, no, why we have to free them.
There. That's what the "abolish dog imprisonment" movement could be based on, if you want to use it. If you don't go at least a little dark the "abolish dog imprisonment" movement will have no teeth (and what are wolves without their teeth ;) ). The people who read your webcomic will view that movement as a bunch of unsympathetic idiots. Unless that's what you're going for, then ignore everything I just said.