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 phenomenon or ridiculous pseudo-science.
Yes I agree this is a huge oversimplification on my part and I'm no scientist or anything, but I feel like it is fair to say different messages appeal tend to appeal to men and women just because of different brain structures and hormone balances that have developed into the way they have based on historic roles in the human race (way before we had any sort of developed society).
I think you bring up a good point about women voting to the right of men throughout much of the previous century, however, back then left and right were seen as completely different than they are now and the messaging was very different. Previously, the left had been a champion for workers rights, and until relatively recently, men had been a large majority in the formal workforce, especially in dangerous work conditions such as factories. Today, men and women have pretty close to equal employment and far fewer people work in jobs that involve immediate physical danger.
Also if more women were largely contained to their home or local community at most, then a more conservative viewpoint makes sense since they would want what's best for their family specifically and really hadn't been exposed to the outside world enough to develop that deeper understanding of how things are interconnected and that everyone needs help. Nowadays, very few women are truly confined to just the home, and the ones who are still lean heavily right.
These are both huge generalizations, but their generalizations based on history that I think most would agree are fair.
