You can compromise on it, but she apparently won't. Thus, deal-breaker. No one's arguing that it's impossible for them to pick other choices, but this woman chose telling her boyfriend to move out over settle someone lower in the "range of cleanliness." That's pretty much the definition of a deal-breaker...something that you're not willing to compromise on, regardless of whether a compromise could exist.

And as far as pets go, you can make all sorts of compromises. A big dog or a small dog. Indoor or outdoor. Only one or multiples. Get a puppy or an adult dog. Lack of training or completed obedience school. There's a huge range dog ownership. Having a low-key dog that stays in the backyard is very, very different from having several large and/or high-energy indoor dogs. A person who's anti-dog might be willing to make a compromise on the former but not the latter, just like a neat freak might be willing to compromise on when the dishes get done. I personally don't have any position on the dog spectrum where I'm willing to compromise, (like OP's girlfriend apparently feels about cleaning), but that hardly means that the entirety of dog ownership boils down to a single binary "yes" or "no."