I too always got the impression that 'cancellations' were spearheaded by young, leftists. Not sure where gender comes in to play though.
Although you could make an argument that it still leans left on the public side, with more of a focus on private death threats and harassment on the right. They don't approach the problem of crushing dissent with exactly the same strategy.
women tend to be more left leaning than men.
https://www.economist.com/cdn-cgi/image/width=360,quality=80...