If you only used a better slogan, people would just magically be on your side
America legalized abortion and banned leaded gas around the same time. Both were credited with lower crime and violence rates in the following decades. Looking at other countries that did not do both so close together it becomes a lot clearer that both made us safer.
I'd also argue that being further removed from WW2 vets and cold warriors with severe PTSD and government mandated drug addictions generally help. Last bit it decidedly my opinion.
Abortion and by extension or related to it birth control pill (and later methods) is an interesting thing I hadn't considered.
It took someone pointing it out for me to consider reproductive choice being related societal violence even though I knew choice was better for societal economic outcomes.
Given the shift to confront, stop, and treat all forms of childhood abuse rather than ignore it also had to help. During the satanic panic the administrations stance was to blame mothers for failing to take care of their husbands as the root cause of childhood abuse. They had the data that showed abuse was linked to poverty more than anything else but it was cheaper to blame women. We're still not in a great place when dealing with childhood abuse but we're better than that and it has to have done something.