My grandpa killed a dog that bit me when I was a toddler. More accurately it kind of mauled me and I have scars on my face from it. I don't care to dive into the details of Noem's case (or debate how my grandpa managed his dog) but I don't think farmers killing dogs is quite as uncommon as the reaction makes it seem.
She wasn't exactly a farmer
She sounds like more of a hobby rancher in the Land of the Cheap. But the optics of it are crap. Yes, cats kind of suck. But anyone who can't connect with a dog is a sociopath, IMO. I also recognize that rural types sometimes view dogs as mere property that they can dispose of willy-nilly. I, and many Americans, do not share that viewpoint.