If this were true, countries like New Zealand, Sweden and Australia should show higher rates of familial breakdown and violence, right?
Not at all. The assumption that is made with that position is if there are no Christians, there is no God. But no... God still moves on people and depending on the bent of the heart, the quality of life.
My wife and I didn't know Jesus intimately until we were in our mid and upper 20's but we were still being moved on by God's Holy Spirit. In our families, both my wife and I were the ones who were more bent towards God.
One day, when my wife was young, she noticed that her mom's face was slowly looking more and more like a picture on a demon book. Her mom was involved in witchcraft.
Living in a dilapidated Spanish colonial style home, her mom rented rooms out and all the families shared a 55 gallon drum for a garbage can. As her mom was out, she unloaded the garbage, put over a dozen witchcraft books into the bottom of it and rolled out the 55 gallon drum to the street side so that the garbage collectors could take it away.
She may have not known Jesus intimately, but God was still moving as God loves all people. Her tender heart was still being influenced by God's Holy Spirit. So anyone can still have a better marriage and less violence if hearts are bent towards God even if they still don't know Him intimately.