I suspect pushing sexism underground sometimes actually creates more anger and misogyny and I don’t have an answer to that.
Yes, I think this is true and it can be quite complex. A lot of lefty men think they are not sexist at all, or that sexism is over and women have equal rights now, and cannot see or understand their own misogyny - being left-wing and therefore right on and morally superior means they can't be sexist. But often they're just suppressing it and it comes out in anger and resentment towards women, who, at some deep level, they still actually do think should be serving them, doing the childcare and housework and enabling the man's career, and providing regular sex, and not getting above her station by earning more or having career status.
I'm not saying all left-wing men are like this but I've known so many who are. Often you sense a coiled spring of anger under a veneer of Mr Lefty Nice Guy. Often Mr Lefty Nice Guy's family set-up is oddly traditional with the woman doing all the gruntwork and taking a back seat in decisions and her career getting sidelined. That happened to me in my relationship and I thought I was a lifelong radical feminist - it took me so long to see that I wasn't going to get through to him, he wasn't just scatty - he was deliberately, if not necessarily consciously, keeping me down and using my labour to benefit himself.
So it doesn't surprise me that men like this, including my ex, love gender ideology - a worldview that lets you look virtuous and inclusive while simultaneously finally getting to tell women to shut up with impunity.