"So why don’t they join forces, rise up against the patriarchy? Imagine what the women of Gilead (or anywhere) could accomplish if they turned to each other, rather than on each other."

Setting aside the implication that women appear to be women's worst enemy (queen bee syndrome) funnily enough, there IS such a tale in existence.  It was written 2400 years ago, and I suggest the author read it.  It's called Lysistrata.

But since it was written by a man, I suspect it won't pass muster.