The first "discussion" shut down by political correctness is airport "profiling" - the left in America would much prefer that everybody's grandmother and 3 year old toddler was strip searched and molested by TSA agents than do what the Israelis do at their airports - they target and watch out for those who are in groups known for terrorist activities and that are travelling alone, etc. Do that in America and the left and the ACLU is out in force claiming racial profiling and using that to shut down the discussion by claiming anyone who wants to profile is a racist.
The second "discussion" shut down by political correctness is related to gun control and gun violence and the actual prevalence of guns used to murder and cause mayhem among black and hispanic youth, in gangs, in major cities. The left likes to cite gun death statistics as a reason to control gun manufacturing and possession when by far the vast majority of deaths due to gun violence is black and hispanic youths killing black and hispanic youths in inner cities in North America, and most of these crimes are committed with handguns, not assault weapons, as the left would like you to believe.
I could go on, but that's example enough.