They aren't partiarchal in a sence of the rule of the pater familia, they are in a sence of a brotherhood of emancipated "sons", who just now are getting power and resources. Because moids are moids, women to them are resources and they aren't letting go of any of their new shiny power.
Yes, racism and homophobia (agains gay moids) are crimes in modern american "left", but they hate women all the same and their "anti-capitalism" party line is basically incomprehensible. They sabotaged their own shot at revolution for restoring full male privilege within american hegemony.
Historically speaking, various tyrannical empires did have different definitions of a "nation" that comprises it, so the dominant class can be reformed to include men of certain confessions and races, and plenty of patriarchal dystopias accept to a dergee of men who use other males sexually.
You won't generally see lefties grilling black dudes for misogyny against black women, or liberals calling for gays to support lesbians. It's not on the agenda. You will see however some dudes complaining that black men are jailed for sexual crimes whitey men get away with (Unfair! It's our turn!) and "LGBT" activists promoting gender roles, gay male hypermasculinity, BDSM as an expression of those and other shit.
They have to make some compromises because they're underdogs in the grand scheme of things, but moids are moids. They consider basic women's safety and freedom to be conditional on her "moral goodness" and that hinges entirely on her schizophrenic self-defeating loyalty to moid doing the judging. On the left as on the right.
I don't even fucking know where does shoe and her clones fit on the political spectrum except being pro male supremacy, which is every part of political spectrum.