Mixed answer from me, in that, while women do seem prone to SJW-ism in general and genderism in particular, the reasons for it strike me as the opposite of the Orwell quote.

Winston Smith's perception is that women are enthusiastic supporters of authoritarianism. But of course... this is from a work of fiction, as well as a specific character's perspective (which turns out to be wrong, actually, at least with regard to Julia, who is in fact an undercover rebel). In real life, what I've noticed is that women tend to be ANTI-authoritarian. The ones who don't support "Big Brother". It's men who are much more inclined towards authoritarianism; by contrast, the liberal/progressive contingent is always predominantly female.

But how does that square with women's penchant for SJWism, you ask? Well... I think the answer lies in their perspective: the way that they see themselves, and the cause that they're espousing.

To me, it looks like they're anti-authoritarians-- liberals/progressives-- who've mistaken transgenderism for being on the same "side". Probably because it's presented that way, and they just assume that "men in dresses" = gender-nonconforming/gender-critical (ah, the irony...). Therefore, they think that they're "fighting the good fight" against pink-is-for-girls/blue-is-for-boys, traditionalist, restrictive attitudes, in the name of all that's liberating, open-minded, and egalitarian.

So I think that it's less a case of women having a naturally-authoritarian bent than that, sometimes, anti-authoritarians just have really piss-poor analysis.