Are you saying that, for instance, if Hank Green were to correctly call someone's words racist, and that person were to complain to Hank Green that this labeling hurt them, Hank Green would thereupon feel bad, apologize, and refrain from using the word "racist" henceforth?

I guess he would. Well, at least if the complaining person was a woman, or black, or disabled, or homosexual, or whatever. He would probably not stop using the word "racist", but he would be more careful to use it in a way that makes obvious that the word applies only to white straight males.

Ok, I was joking here, but here is a thing that really happened on a feminist blog: There was a discussion about trans people. All people were super politically correct, except for one person who repeatedly asserted that trans people are against the nature, because the Spirit of Nature told her so. When other people finally attacked that as cis-ism (or how exactly they call that), the person defended by saying that she was a Native American, and those were her Native American beliefs; and that the people who offended her beliefs should check their privileges and apologize. And... however incredibly that felt to me... they really apologized. I was completely shocked. So yes, this kind of behavior really is possible. It might not make sense to you or me, but it exists.