I have studied the problem and thought quite a lot about it. I think sexism will tend to persist because there are biological differences that have substantial impacts.

The fact that women can get pregnant but men cannot has a huge raft load of implications that influence the attitudes and choices of both men and women. Women I have known who thought they could live their life like a man did fine until they had a baby, at which point their assumptions of independence and self determination had an unpleasant wake up call.

There may be things society can do to mitigate that reality, but most discussions I see of gender equality make zero effort to mitigate it. Instead, most people seem oblivious to its existence. This does not bode well for the possibility of creating policies that genuinely help level the playing field. I believe there are inherent challenges in creating good policies in this area, so it likely won't happen by serendipity.

The current result seems to be a growing divide between the quality of life for empowered women and disempowered women. That divide seems to be strongly influenced by reproductive choices in ways that are not obvious or straight forward.