Liberal views are increasing over time

Here's at least one that isn't:

https://www.washingtonpost.com/news/volokh-conspiracy/wp/2014/02/17/growth-chart-of-right-to-carry/

This is also complicated by the fact that views that go out of favor tend to be characterized as not liberal regardless of whether they actually were liberal. Eugenics is one of the better known examples.

I can't find any studies, but I predict that if we do a study, we'll find that holding the belief "women and men are equal" is strongly correlated with being non-violent and not hurting women, and almost all of the violence and abuse cases committed against women will be by people who don't think they are equal.

Saying "I don't have a study, but I predict that if I do a study I will see X" is no better than just asserting X.

Also, "women and men are equal" is vague. Do you want equality of opportunity or equality of outcome?

Even "violence against women" is vague. ISIS likes to kidnap women, but they also like to kill all the men at the time they are kidnapping the women. So ISIS causes the absolute amount of violence against women to increase, but the relative amount (compared to violence against men) to decrease.