The case you are referring to is definitely political correctness gone off the rails. I have no problems accepting that some political correctness is corrosive. What I have a major problem with is that many right wingers, such as e.g. Jordan Peterson, try to create a narrative where political correctness is one of our biggest problems.
I think that is completely off the rails. Racism, bigotry, nazism etc is still much bigger problems in todays western society. More people are killed by far right terrorism in America today than Islamic terrorism. I feel that many of the right are trying to create a false equivalency between the problems on the left and those the right. In the 70s and early 80s, left wing extremism was an actual problem. There were leftist terrorist groups such as Rote Arme Fraction. We must reckognize the the main threat of extremism today is in fact on the right.
We cannot use once a blue moon occurances to claim a moral equivalence.
The 2nd one is an explanation why a tolerant society must allow Intolerant views to be spoken, as long as there is no violence with them.
My discussion of being intolerant towards the intolerant means something quite different though. The problem is when we self censor ourselves to be tolerant towards narrow minded and intolerant views. I am in particular thinking of religion. Religious people tend to be handled with silk gloves in public discourse. When did a mainstream politician e.g. ever call out what is going on in many religions? People are afraid to talk about the attitudes towards women, gay etc within many religions. Or one dears not speak up about the many superstitious ideas such as homopathy and healing.
In Norway we had a princess, who started an angle school. Nobody really deared to criticize that in public. Not because there are laws against it, but because people are so eager to be tolerant towards any crazy idea.
My idea of being intolerant towards the intolerant is not so much about laws, as it is about what sort of behavior we should encourage. In Norwegian school we learn about all world religions. I think that is good. However only learn to be understanding and tolerant. I think it is important to also learn how to be critical, and not just friendly and tolerant.
Speaking in a respectful and serious manner, should be encouraged, but it should be possible to disagree with each other without offending the other person.
My point is that this goes both ways. It is not just liberals in college who have to give up their safe spaces, but also the religious which must accept criticism of their faith, and accept that atheists and other non-religious people have as much right to be heard and respected.