I think a useful, natural definition is where there are social mechanisms to reduce the expression of an idea for reasons other than its utility in creating the most accurate models of reality. It’s not that the idea is empirically incorrect, it’s that it’s politically incorrect.
That is, the reasons for the suppression of the "politically incorrect" statement, by various social mechanisms, are unrelated to the truth value of the statement.
The (implied) definition of the social mechanisms to reduce the expression of the "politically incorrect" idea is very close to Harry Frankfurt's definition of bullshit: bullshit is, says Frankfurt, not a lie, but a statement which, while outwardly protesting concern for truth, is actually utterly unconcerned with truth. The liar is at least conscious of the truth enough to formulate a lie; the bullshitter eschews even a conception of the truth.
But is the "politically incorrect" really so broad? Certainly, all objections to genuinely politically incorrect ideas on the basis of political correctness are bullshit, but certainly we can't say that all bullshit objections are objections based on political correctness. As TGGP puts it,
So, could good etiquette, which often means avoiding frankness or expressing thoughts even if others suspect we have them, be considered a form of political correctness, even when it has no connection to policy?
A few years ago, I was riding in a car with a friend who has Asperger's, and another friend who doesn't have Asperger's. The non-Aspie friend made a kind of offhand, lame joke, and I laughed. My Aspie friend asked why I had laughed, since the joke wasn't funny. I explained that laughing at jokes is a socially polite thing to do - like saying "bless you" when someone sneezes, regardless of a belief in God. He seemed to understand and for the rest of the ride, he practiced "polite laughter" - it was a bit ghastly, really. Anyway, my laughing at the lame joke was certainly bullshit - a response unconnected with the truth, but engaged in for some other reason (politeness). It wasn't a lie, because I laughed even before evaluating the merit of the joke. But I think few of us would classify my response as the "politically correct" response. Only a subset of bullshit is politically correct bullshit.
I, for one, often feel the need to liberally coat my politically incorrect beliefs in charming bullshit in order to make them more palatable. I think, in this case, the motive is politeness - and an eye to genuine communication - ideas can be more or less understandable depending on their presentation and context. But even ideas that are not politically incorrect may need to be ensconced in bullshit for maximum communicative value.
We can get closer to a phenomenological definition of the politically incorrect. Folklorist Linda Dégh might be regarded as an expert on the folkloric legend, as distinct from märchen, magic stories that we might refer to as "fairy tales." The main difference is that the legend is a personal story that invites genuine disbelief (think "urban legend"), whereas märchen are impersonal stories that are clearly not intended to be believed. In discussing the definition of the legend, Dégh says that there are some stories that she excludes:
Arguing for the disputability factor as crucial, I excluded legend-like narratives that enforce belief and that deny the right of disbelief or doubt, narratives that express majority opinion and are safeguarded by moral taboos from negation and, what is more, from deviation. ["Tape-Recording Miracles for Everyday Living," in American Folklore and the Mass Media, Indiana University Press, 1994. Emphasis mine.]
Dégh's examples are "religious (Christian, hagiographic, or saint's) legends," and the "patriotic (heroic) legends dispensed through school education by governments, confirming citizens in civil religiosity."
I propose the following: For an idea to be genuinely politically incorrect, (a) the idea must be in conflict with majority opinion, (b) there must be social mechanisms to reduce expression of the belief for reasons other than the idea's truth value (i.e., bullshit is set against it), and (c) these social mechanisms must have the function of a moral taboo to protect an important cultural narrative from negation.
Interestingly, my requirement of being opposed to "majority opinion" would exclude from the "politically incorrect" cases where people speak out against the narratives promulgated by their government, if the narratives are not believed by a majority of the population, as with Chinese dissidents challenging Mao's bullshit about the man-made famines of 1959-1961 and beyond, and opponents of the war in Iraq today.