Feminism is not about equality and has not been since the 1960s. So-called ‘second wave’ feminists abandoned all pretence of that. Instead it became about women having power; not just equal power but total power. Specifically, power over men.
Feminism is fundamentally anti-democratic, because it is rooted in Marxism, which is against democracy. However, this form of Marxism is not identical to the original materialist one; it has been modified because women rank social power more highly than material wealth. So the original economic form of Marxism was modified using another philosophical system, this time called Postmodernism. This ranks everything and everyone in terms of social power.
The New Atheists, like Richard Dawkins, Sam Harris, the late Christopher Hitchens and many others, purported to offer a sane, secular attempt to roll back religiosity for the betterment of society. Instead, their efforts have begat the mother of all calamities.
How did this come to pass?
Scientific atheism, as promoted by the New Atheists, lacks any unifying central structure or code. Essentially it is based on a negative — not believing in God. So it can’t have a defining structure. Richard Dawkins, one of the most prominent New Atheists, tried to answer this with his ‘brights’ — which was an embarrassment. (Since at least 2014, Dawkins has self-identified as a ‘secular Christian’ anyway.)
After the Enlightenment and especially the French Revolution, European secularism based itself around Reason as the core methodology that would replace, in the minds of those who were atheist, religious belief. This reflected a rejection of hierarchical religious authority, which had begun in the Reformation. The works of philosophers like Descartes, Voltaire, Rousseau, Kant and Paine promoted the idea of the free-thinking individual whose intellectual scalpel was Reason. Both of these were exported to the US.