Political correctness is a curious phenomenon. Supposedly it took its name from an inside joke in leftist circles stabbing at orthodox Marxism, which dogmatically judged political positions for their "correctness" in relation to doctrine.
It seems like the right uses it more than the left now, not as ironic reference, but as a weapon to break down policies, actions and language that presents a resistance to their projects of domination.
"Their projects" is the key designator here. This divide is illustrated by leftist practice. When it comes to what is referred to as politically correct language and practice, language and practices which are offensive to white people are generally not taken as seriously in leftist circles.
Mere offence is not what is being avoided here, but the offence of the oppressed. Politically correct language is a form of eliminating the offence of the oppressed, on a linguistic and ideological level, and then an emotional and physical level by extension. The general project is protecting the oppressed from any more harm, and buttressing their position in the body politic, which is a project that is peculiar to a particular time or stretch of time, and place(s).
Of course it isn't like I'm making a staggering political discovery by claiming that offense itself is heavily reliant on political relations and power.