There are many historical factors that we may not even be thinking about. GB talked about immigration and drugs, someone mentioned abortion for the recent decrease in murder rates. We could also mention that there's a big history lurking before the sixties. Perhaps, as you said, there were tougher moral doctrines imposed on everyone, and so the thought of shooting people was supressed more efficiently. Perhaps the hippy times did unleash unpleasant hidden violent drives that suddenly stopped being so suppressed.
But it could also have to do with the second world war' long term effects on the population (perhaps the violent people of that generation were most likely killed or traumatized during the war, perhaps many other explanations). Or it could have to do with the sheer optimism in the 50s that the crime rates in that decade were so low then. The seventies were very pessimistic, by contrast. We had peak oil, mad max scenarios to look up to, usa had vietnam, the cold war, etc. Blacks also started to make a fight for their rigths and that involved a lot of violence too.
Idk, I just see so many variables, that to try to pin it down to a simple explanation of the thing really needs a ****ing brilliant mind.