"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.)