I think if you look at a couple of posts earlier, it's also easy to offend by being too pc. One poster talked about being patronised. It's not necessarily about being polite. By being "pc" one can just as easily be addressing people as a "type". Eg you are from India therefore you come from a poor background therefore you must be more intelligent or must need to be treated more gently or you are Muslim and therefore easily offended etc etc. It is to do with a combination of sensitivity and common sense.
I also think there is a little too much stereotyping of people who resent "pc" ness. I don't think it should be forgotten that there are people who have a certain background who strain against that and have a good will but are uncertain in how to deal with issues which they have no familiarity with at all.
For example there will be many adults and especially older people whose children have grown up with multiculturalism and multisexualism (?) and who know, intellectually, the "correct" approach but for whom it doesn't come naturally. Hence the awkward family members being overfriendly with gay boyfriends and so on. It may cause eyerolling but it comes from a good place.
For children who have grown up completely multiculturally it is natural to say, the Korean girl, the black guy, if they are used and useful as swift identifiers, just as they would be called the English boy, the white girl. But it can feel very, very awkward if you haven't, it can sound very racist.
The resentment of pc comes in part from a resentment of being told what to do, what to say and what to think, possibly even more than what they are being told to do, say and think.
In addition some of the things one hears "pc" tales about are very urban: there are still parts of the country which are do not have that urban mixed culture.
My own take is that eg I grew up with absolutely not one single friend who was not white, there were two black children in my school and they were boys and not my year. But I was "educated" by my parents about equality so it was less natural and more intellectual, until I gained my mixed bunch of friends moving to London. Whereas for my children, who have friends of multiple nationalities
and races (at one party every single child was from a different country) it is inconceivable that anti-racism would have to be "taught" to them. I would have to actively teach them to be politically incorrect.
It is far the better way, than telling or teaching people what to say and think, and I believe this is where some of the resentment comes from.
Of course some definitely comes from racism and prejudice about sexuality and religion.