As a woman and a white person who decidedly does not hate black people, if I overheard someone saying 'White people are racists!', I'd probably want to pull a 'not all whites', to be honest.
I get what the author is driving at, that this potential swing in cultural terminology is no doubt an improvement for feminists/activists, but I do have to wonder. Mocking and (in effect) punishing those who do this seems to me to be far less likely to draw someone to your viewpoint, and more likely to push them to hold the opposite. If you expect your audience to "check their privilege(s)" and be mindful of others, you should probably endeavor to do the same in your own words and actions. This doesn't mean every intrusion into a conversation should be coddled and the intruder be patted on the head for their good intentions, but it does require a modicum of genuine empathy to avoid pushing that person further from your presumed goal.