I wrote about the views that all the new right-wing authoritarian movements share about women in a post last December, and also a year ago, in August 2018. Neither post, sadly, is out of date today.
That last August post, in particular, delves into the question why very different types of authoritarian movements, from ISIS to US Proud Boys, share the same basic view of women's proper roles. One possible theory:*
The very definition of ideal masculinity in the right-wing movements can also cause this:
The ideal man is a virile, violent and fit patriarch, and that ideal can be magnified and made sharper only by denying women any roles which are seen to infringe on male prerogatives. This is because masculinity in those movements is defined as subtractive: It is what women should not be or what women cannot be.
Thus, to increase the power and space for men, it's necessary to enlarge the sphere of masculinity and to shrink the sphere of femininity. In the most extreme right-wing movements women are strictly limited to their reproductive roles and kept out of public spaces.
That prescription may sound particularly appealing during times when those men who already have right-wing values feel that their dominance is threatened, that they are slipping down the rungs of societal power ladders. This could explain the appeal of far right movements to some American white men with conservative views, given the changes that outsourcing, globalization and recent immigration are causing in the society.
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* Go to the original link to read the footnotes those paragraphs have attached to them. I removed the asterisks here to make the quote look cleaner.