Fear of political incorrectness

What can we call people who have a debilitating fear of saying or allowing-to-be-said anything that's politically incorrect?

I can't use the terms "real", "truth" or so because it's not necessarily proven yet that the politically incorrect thing in question is real or not. It's just politically incorrect. It could be wrong or right - it's not known yet.

We do have terms and labels for the people saying politically incorrect things : iconoclast, conspiracy theorist, etc. Lately even words like Nazi, racist, sexist, misogynist, homophobe etc have been appropriate to attack people saying politically incorrect things in those specific topics. 

Sometimes with funny consequences : like labelling gay conservatives as homophobes, or black free speech activists as racists, or women arguing for equality between the sexes as misogynists, or people disagreeing with some aspects of climate change narratives as flat-earthers.

But can we come up with a term for the people who have an overblown tendency to distribute these terms and labels, who like to go around slamming adverse labels on everyone that they disagree with so as to malign them and shut down any chances for their arguments getting a fair hearing?

I'm open to suggestions!