I see the commentary so far as fairly puckish, and hardly violent.
I personally choose not to take Peterson too seriously on a broader level as he is a clinical psychologist who is taking it on himself to skewer 21st century society with pop sociology hot-takes. The indignance from himself and his supporters about how misunderstood he is, when he has such a strong platform to speak on and is quickly becoming one of the most well-known psychs of the 21st Century, is so, so obnoxious. There is some confirmation bias at play here, but I notice other commentators who specialise in conservative public intellectual hot-takes, have a tendency to victimise themselves when people react to their assertions with "toxic" "vicious" responses, it's a classic defense mechanism that doesn't really work when you have a powerful platform (or works really well depending on your perspective). A recent example being Katie Roiphes hot-take Harpers piece on Twitter feminism, much of the premise I can somewhat agree with, but she paints herself and her interviewess as victims oppressed by "The Culture" and twitter thought-police, when she personally engaged in under-handed tactics exposing someone which resulted in death-threats to them, and is getting published in Harpers, New York Times, being interviewed on CBS, wrote an infamous book in the 90s challenging the number of campus rape allegations being reported (why???), and that's all im really familiar with, but the point being she has a history of positioning herself as a contrarian, asserting she is being persecuted for her opinion by a toxic cabal of activists when she has a precedent for toxicity herself and her voice is hardly being held down. There is little more obnoxious than throwing stones, then being indignant when they're thrown back.
https://harpers.org/archive/2018/03/the-other-whisper-network-2/.
Further regarding my opins on Peterson; what he argues for, and how he argues it, is sometimes as reactionary, inflammatory and misguided as parts of the reactionary culture he rails against. Many of his arguments, and discussions of sociological phenomena to me seem like the academic equivalent of saying "just walk it off" when you have a broken leg. He is a clinical pysch, which focusses on individual treatment. The simplicity of the lipstick debate is so lazy and self flagellating. He doesn't even seem to care, and sounds like a frustrated frat boy on debate night. I also find his broader arguments benefit an adherence to tradition, and prudishness I personally don't vibe with.
There are so many factors which comprise our identity culturally and individually, and there are other public intellectuals whose opinions I'm more inclined to listen to that have dedicated their lives to solutions and allying themselves with progress, rather than making a name in adversity to improving rights for the oppressed. Though considered flawed (according to some psych major friends, i mean, it's a social science after all) I really love Claude Steeles work on Stereotype Threat. I believe true understanding of society will come from arduous study presented in a constructive way, with a willingness to accept where your assertions may be flawed.