Eh, first of all I'm not American so I have very little insight into the day to day on American campus. But I am from a "woke" nation in the form of Sweden.
The three "untruths", god damn I hate when authors write like that, are:
The Untruth of Fragility: "What doesn't kill you makes you weaker."
The Untruth of Emotional Reasoning: "Always trust your feelings."
The Untruth of Us vs. Them: "Life is a battle between good people and evil people."
And they're just so basic and completely miss the point in the case of number two. In fact I'd argue the issue now a days is that we disregard feelings too much. Not from a reasoning standpoint but from the standpoint of what is "true" to me, personal morals etc. People try so hard to reason their way out of situations you need to emotion your way out of. Like relationship troubles.
For "Us vs Them" all I can garner from what they write is that they think we should listen to bigots because there might be merit in their reasoning. And that standpoint is about the most insidious shit there is. While I agree that silent treatment ignoring sentiments like that isn't very good or effective, it's even worse to engage in proper debate when one side doesn't argue in good faith. Don't wrestle pigs and all that. The best way is to kill the debate the instant intolerable shit is spewed and explain that those viewpoints are unacceptable and intolerable. We can't tolerate intolerance to death. All it ever will do is make it seem acceptable when it isn't.
That leaves us with the fragility untruth. And here I see at least some merit. The extreme levels of fear in society in general (when we're by most metrics safer than ever) spewed on by media and news in all forms is making parents safeguard their kids from life. Ultimately leading to kids missing out of a ton of self-exploration and learning from mistakes. We're also far to harsh on kids doing and saying dumb shit, while being to tolerant of adults. When kids say racist shit they need to be taught that isn't OK and why. When adults to it they need to be told in no uncertain terms that their behavior is unacceptable and they're not welcome until they change. Today we see far to often people writing of kids as unfixable when they're 13 like they themselves weren't shit stains at that age.