The anti-woke train has a lot of steam because humans are great at recognizing patterns over time, and are evolved to do this, which is why this stuff eventually reaches WaPo, NYT, et al.
Regardless of whether that is true, I'm not talking about the merits of Peterson's "anti-wokeness". Instead I'm pointing out that it is the foundational component of his following and he actively cultivates this.
I think Peterson would say he is simply the beneficiary of handling it correctly when Woke Culture attacks him, and his public persona with respect to wokeness has been shaped more by their actions than his. Personally I'm not sure - is there a clear action of his that you'd point to as cultivating an anti-woke bent or is your assessment based more on outcomes?