A political correctness (without hypocrisy) feels from inside as a fight against factual incorrectness with dangerous social consequences. It's not just "you are wrong", but "you are wrong, and if people believe this, horrible things will happen".

Mere factual incorrectness will not invoke the same reaction. If one professor of mathematics admits belief that 2+2=5, and other professor of mathematics admit belief that women in average are worse in math than men, both could be fired, but people will not be angry at the former. It's not just about fixing an error, but also about saving the world.

Then, what is the difference between a politically incorrect opinion, and a factually incorrect opinion with dangerous social consequences? In theory, the latter can be proved wrong. In real life, some proofs are expensive or take a lot of time; also many people are irrational, so even a proof would not convince everyone. But still I suspect that in case of factually incorrect opinion, opponents would at least try to prove it wrong, and would expect support from experts; while in case of politically incorrect opinion an experiment would be considered dangerous and experts unreliable. (Not completely sure about this part.)