Labelling speech as "politically correct" suggests that the speaker is being timid and too deferential.

That the sentiment is 180° wrong. Framing things in terms of "politically correct" suggests that people should feel free to say the first thing that comes to mind. Framing things in terms of privilege suggests that people should put a lot of effort into seeing past their privilege:

There isn't really much middle ground here between these two viewpoints. One says you should work hard, the other says you shouldn't.

Political correctness is often used as a pejorative, but like many pejoratives, it can be reclaimed: