All the PC/intersectionality stuff doesn't impact literally 99% of Americans, so no, no one gives a shit about this stuff. It's just in a few areas of a few big cities and specific websites. People aren't walking around worried about forgetting to ask what someone's pronoun is. People aren't walking around explaining how they're trans and what that means. They just are and most people either ignore it or just go with it because who gives a shit.
As for Peterson, he all but admitted to being a scammer in that NY Times piece, at least admitting to putting on a character and selling what his audience wants to hear. And as his audience changes, so does his messaging.