Your criticisms are not surprising given that you have missed the point entirely. In fact, you missed it so badly that your article actually highlights the commercial’s validity.
The idea was not to put all ideas, good or bad, progressive or bigoted, on equal footing. The point is that we humans all have more in common than we sometimes realize. We tend to prejudge and categorize each other based on appearance or opinions, without acknowledging that who we are and how we think are largely the byproducts of our individual experiences. By taking the background noise of those prejudgments out of the equation, and introducing two people who know nothing about each other to a common task, the commercial demonstrates just how much we really are alike under the skin.
As the conversations grow deeper during construction of the bar, the common threads of humanity become even more evident. The transphobe learns to see the object of his bias as a person first. The sexist learns to see the feminist as something other than a ball-busting man-hater. The climate change denier finds common ground with the tree-hugger. And, just as importantly, the individuals with the more liberal views realize that their respective partners in the project are not necessarily the knuckle-dragging neanderthals they would have imagined.
Separating our /acquired/ ideas from our /innate/ humanity is the point of the commercial. You chose to go straight to the “us vs. them” mentality, and in doing so made yourself a perfect, if unwitting, example.