Here's National Election Survey data on voters' view of the question of the role of women in society. Specifically, "Some people feel that women should have an equal role with men in running business, industry and government. Others feel that women's place is in the home. Where would you place yourself on this scale or haven't you thought much about this?" The question asks you to locate yourself on a seven-point scale, I've graphed just the two extreme values which show a sharp trend in favor of the egalitarian position.
This is one respect, at least, in which the United States has become a far less conservative country since the 1980s. What's more, if you look at these demographic breakdowns you'll see that while a lot of the shift is accounted for by cohort replacement, a lot of it represents within-cohort change of heart.