In 2017, social scientist, Charles Murray, arrived at Middlebury College in Vermont. He travelled to the university at the behest of a student group which has invited him to deliver a talk on his book, Coming Apart: The State of White America, 1960-2010.  However, the move drew criticism from alumni and existing Middlebury College students. Their criticism stemmed from an earlier book in which Murray had argued that the existence of a black underclass in the United States was attributable to genetic differences in intelligence and IQ between African-Americans and their white counterparts. After disrupting his speech to such an extent that Mr Murray had to be taken to a secure room and continue the session via livestream, an angry mob descended on him. The host of the event sustained injuries that meant she had to go to hospital.
By denouncing certain ideas as un-PC and socially unacceptable, as occurred in the example cited above, it legitimises violence against those which hold these beliefs.
Political correctness does not legitimise violence. The response to the case of Charles Murray illustrates as much. Those that carried out the violent and thuggish attacks against Mr Murray and the host of the Q&A were denounced in the media and liberal circles. Their peers penned letters and emails denouncing their behaviour. The violence, even against someone like Murray that holds un-PC views, was not legitimised. It was fiercely condemned.
[P1] Political correctness deems certain opinions socially unacceptable and unfit for public airing. [P2] This legitimises violence against those that hold those beliefs.
Rejecting the premises
[Rejecting P2] It does not legitimise violence.