I think a large part of it has to due with a combination and of culture and biology. Biological women are pre-wired to generally be more caring towards others since their job was to carry the baby and then in most societies they would be the most active caregiver towards the baby. Men on the other hand generally went out to hunt, and were far more exposed to competition with other men. They were also the protectors of their family or community. In the parties today, Ds are generally seen as the more compassionate party that wants to lift everyone up while the Republican Party encourages the "pull yourself up by the bootstraps" ideology of individual people reaping the benefit of their hard work.
Finally, Dems were generally the ones to side more with the #MeToo movement and generally empowering women to enter the workforce and participate in jobs they usually wouldn't participate in. They also tend to stand up more for women who have faced abuse and other injustices.
Somehow this explanation is both blatantly sexist as well as nonsensical when considering the timeline. As others have noted, the female vote was historically right-leaning compared to the male vote. In fact, many left-leaning parties across the globe specifically tried to block and stop women's suffrage because they feared that women voting would tip the scales towards the conservative/religious parties. In the US, women voted towards the right of men until about the 60s and 70s, where there was little/no gender gap.
The 80s and 90s are when women started to sort into the Democratic column. With that information in mind, the cause would have to be derived from that political era.
And there are multiple potential theories: Some scholars have argued that divorce rates as well as the general decline in marriage was a significant contributor. Others have stated that Reagan/the GOP turning against the ERA and similar moves against women's issues pushed women over towards the Dems. And some argue that women had leaned more liberal on the issues compared to men since the 1960s, and so it was all just natural ideological sorting.
Notably, none of these explanations have anything to do with extremely modern phenomena or ridiculous pseudo-science.
