Political correctness exists, but it is rarely properly understood. Although some choose to define it as a "not an asshole" mode of speech and thought regulation, it is much more than that.
It is a method of social conditioning by which an agreed upon "good" speech and thoughts are promoted against "bad" speech and thoughts.
It is nearly impossible to argue that it is an exclusively left-wing affair, just as it is nearly impossible to argue that it is inherently undesirable.
It is, in fact, a ubiquitous method of social control, and will remain with us whether we like it or not.