My dog has a blog. Black Dog Diaries. I take him to the local dog park on a regular basis. It surprises me every time I’m there that there exists the curious implied “requirement’ that all dogs be a “something”.
“What kind of dog is he?” is the question. It’s likely a conversation starter among awkward strangers, but it may speak to the point Ms. DeMarco is making.
I am not in agreement with Ms. DeMarco’s estimate that the question is “both insulting and demeaning”. That may be as much of a overstatement as what the AKC had to say about, “we’re not disenfranchising or specifically harming mutts.They’re still able to find good homes.”
A simple answer to the question of your canine’s heritage is, “He’s my dog. Isn’t he great?”

I think, as evidenced by recent news coverage of dogfighting, that all types of people associate themselves with dogs, some more productively than others. Unfortunately there will always be people that use dogs as status symbols. The iconic nature of DOG exists. Pit Bulls (Staffordshire Bull Terriers ) are the new “bad boy” dogs. I have seen German Shepherds, Dobermans and Rotweillers all play the role, in turn, as dictated by human whim. I find it sad that breeds of dogs are singled out as “bad”. I view dogs as unique individuals.
I think there are plenty of dogs to go around. The world doesn’t need to breed more, mutt or purebred, until we can understand and take care of the ones we already have.
I strongly advocate spaying and neutering, but have included a link at the top of my comment that leaves that advocacy open to examination.

I may be more in agreement with Ms. DeMarco than not, but the language used to create the discussion may be as ineffective in gaining cooperation as beating your dog is to train it.