Much of what I have observed involves suppressing inconvenient truths, not so much to avoid hurting feelings, but to avoid openly contradicting people in authority, like bosses, teachers, committee/team leaders, etc. Challenging the worldview of these authorities has obvious risks, which not everyone is in a position to accept.
Many of my examples occur at work, where the work environment is filled with rules and regulations that cost time and money while contributing nothing to getting the job done. It is politically incorrect to point this out, however, especially when higher-ups are visiting, or we are getting site inspections. These folks don't want to know what it costs, or what isn't getting done because of it. They just want to see everyone following the rules.
It is politically incorrect to point out how another employee is not doing their job, especially without offering up some sort of "mitigating circumstances" that may not even exist. It is even worse if you want to identify a low-performing group, such as "graduates of University X" or "the purchasing department".
It is politically incorrect to suggest that our annual fundraisers for various charities are not at all efficient in raising money; or that we could easily cut the cost of the holiday party in half without sacrifice of content; or that no one is interested in the prizes offered as quarterly awards. Each of these claims suggests that Someone Isn't Doing A Good Job, and we're not allowed to say that.
My current workplace is particularly bad about all this, but I have yet to work anywhere that does not have some of it. I see also in churches, volunteer groups, and especially in schools. Every so often, someone is brave enough to speak the truth. Sometimes it is received better than they expected. More often it is openly criticised, quietly suppressed, or persistently ignored. I pick my battles carefully here because I have only so much political capital, not to mention time and effort, to expend. I go after the things that make the biggest impact on my work, and succeed often enough to be willing to remain in my current position, for now.
Interestingly, the one place I saw very little political correctness was when I worked in a political campaign office! Perhaps that organization was just too goal-oriented to worry about it.