Women are, fundamentally, conformists. That is, they choose the “handshakeworthy” option largely regardless of ideology.
In the West that would be the culturally pozzed mainstream, i.e. anything but nationalism or the hard right.
This explains the Alt Right’s dim views on women in politics, culminating in memes like “thot patrols” and “white sharia” at its extremes.
However, what constitutes “handshakeworthy” has differed down the ages.
Two to three generations ago, it was well known that European women voted relatively more for Christian conservative parties. In most countries, more women than men consider themselves religious, while far more men subscribe to outright atheism; a vast socio-demographic echo from centuries past, when religion was the bedrock of society as opposed to just another consumer item.
In Russia, the handshakeworthy electoral choice is the conservative/patriotic “party of power” United Russia, but not so much the nationalist LDPR, the communist KPRF, or Navalny’s liberals. Even so, as Vincent Law points out, Russian women are not any more pozzed than the men. This is a true observation, and it is reflected in political participation. While the American Alt Right is pretty much entirely male (when I met up with Richard Spencer & Co. in 2016, there were just one or two women out of fifty people, as I recall), in an equivalent gathering of Russian nationalists they’d constitute perhaps 20%. Which is about reflective of default male/female interest in politics, anyway.
Almost no women voted for the Nazis in the 1920s, even relative to the men, when they were still considered a freak-show; however, many more of them voted for religious nationalist parties, while far fewer voted for the Communists, while support for the Social Democrats was about equal across sexes. However, by the time of Germany’s last free elections, support for the Nazis by sex was equalizing. If a free vote had been held in Nazi Germany by the late 1930s, I suspect Hitler would have done relatively better with the women.
It is pretty incontrovertible that women tilt moderately left relative to men on economic matters. For instance, the historical extension of female suffrage in the American states was associated with the accelerated growth of the welfare state in those regions (Lott & Kenny 1999). (Though given the absolute barebones state of the safety net before that time, it’s not obvious that that was even a bad thing). This is also why I suspect that there was virtually no sex gap in support for the statist Marine Le Pen in France, versus a huge gap in support for the arch-capitalist Trump in the US.
I am not making any sort of normative point here, just pointing out how things work.