It is normal wanting to hurt people that hurt animals so badly

Animals dont think the way we think. Therefor it is easier to see them as non deserving of certain human behabiour than other humans. The desire to protect them is nothing bu logical thinking

Yes, it's completely normal for both rational and emotional reasons. Rationally, people who hurt animals for their own entertainment are waving some really big flags that they're going to start becoming a danger to people one day. Hurting animals is an early warning sign along the path to raping, torturing, and killing other human beings. Emotionally, a lot of animals (including domestic dogs) trigger a lot of the same thoughts/feelings as human babies do. Compared to wolves, dogs act more like our children, have bigger, rounder, less threatening features, rely on us more for their well-being, etc. Rationally, we know they're not really our babies but emotionally, they kind of are, just a little bit. The natural emotional response to seeing someone hurt a baby is to destroy them, so the same goes for the dog.