'Killed her 14 month old dog for misbehaving' is the clicky headline. But the subtext is, this person might be the republican running mate, and her story is presented as a parable about how killing is 'a job that needs to be done'. It's not crazy to put those pieces together and be anxious about the direction they point in.
I can see where you're coming from. You're right that her story is divisive. I think that's the objective. It's an engineered, populist, fascist move to present the story in the way that she does. No one in the public eye writes that kind of thing in a book and expects it to fly under the radar.
You're also right that there's a strong rural/urban ideological division. Best way to fix that I think is to talk to each other more, IRL, and try to honestly understand the perspectives of others, especially if they're different from our own. My 2¢.