Actually, no, they seem pretty tied together these days. It's doublethink, to be sure, but they're both now considered the standard for 'decency'... the same people who say stuff like
this or
this are also the ones who rant about rape culture or women owning their bodies.
"Gender is a lie" is, I take it, a caricature of contemporary queer theory. Butler et al. "Womyn power" is similarly a caricature of a certain strand radical feminism. Dworkin et al. But the thing is, these two groups do not get along, at all. They start from incompatible assumptions and arrive at very different conclusions. Further, each branch of the feminist tradition contains often-contradictory currents. Some queer theorists interpret "gender is a lie" as a call to the abolition of gender identity, while others takes it as an invitation to a multiplicity of gender identities. Some radical feminists take "women's liberation" to be a liberation of women from womanhood (traditionally defined), while others take it as the liberation of womanhood, of femininity, from patriarchal constraints. And there are, of course, a thousand other shades between and on either side.
The weird thing is, it would have been easy to get away this, because there are a lot of currents in modern feminism which are not compatible on close examination, and a lot of people don't engage with these contradictions in a lot of depth. A lot of the discussion around trans issues takes gender to be innate, while a lot of the discussion around genderqueer identities takes it to be voluntaristic, and a lot of people will employ, as you say, some pretty heady doublethink to avoid confronting this apparent inconsistency. All of this compounded by liberal feminists who take
any of it terribly seriously, but have borrowed certain vocabulary or reference points from more radical currents because it is very important to appear woke af. (See: the 2016 Clinton campaign.)
But instead, you're lumping divergent and often deeply acrimonious currents in together as if they were the same thing, because all you can see is what they
aren't, that they're opposed to a conservative patriarchal social structure. You're not interested in the content of their ideas or practice, and I'm going to frankly suggest that you don't have the first clue as to the differences anyway, you're only interested in what they represent to
you, in the role they fill in the narrative you've built. The same way that an anti-Communist can look at Stalinists, Trotskyists and Eurocommies, even at milder-than-milk social democrats, and say "yes, these are all exactly the same thing", because what matters to him isn't what they do or say or think, but that they're on the other side.
I didn't pick up this point just to be a pedant- "um, well, actually, Rühle was associated with the Allgemeine Arbeiter-Union Einheitsorganisation, not the Allgemeine Arbeiter-Union Deutschlands"- but because the failure to recognise these fundamental and longstanding division within the feminist tradition reflects a basic misapprehension underlying your argument, that feminism is something external into the culture that has been introduced as a deliberate and foreign influence, a coherent "bandwagon" driven by a definite political will, but the reality is, feminism
is the culture, or at least a part of it, however people happen to feel about the f-word itself, that certain key assumptions of Western culture are by any definition "feminist ones". The discussion is about what feminism looks like, about what these assumptions imply for how the world looks and how the world
should look, not whether feminism was a good idea at all. Those choosing to raise this latter argument, far from the defenders of convention are making an active choice to reject it, to stay behind in a half-imagined past while the world moves passed them- or even, as often as not, the world stays perfectly still and they move further away.
If you want to find an example of wilful and almost antisocial deviation from the established norms of "Western civilisation", you couldn't find a better place to start than somebody like Peterson.
