I think the majority of opposition is not opposition to that goal (though there's some of that) but to the methods. People repeatedly answer in the affirmative to questions that sound like, "Do you want to live in the Star Trek society", but in the negative to questions that sound like, "Shall we get there by saying men are trash, treating people first and foremost based on the intersection of their identity groups not as individuals, and enforcing equity independent of merit rather than developing merit and ensuring equality of opportunity."

Correctly or incorrectly, a lot of the latter stuff has become associated with intersectional feminism.

The part you're selling has already mostly been bought. That this is the product that contemporary intersectional feminism has to offer is what is less clear to people (given polling data, at least).