One who truly believes in God believes in justice, love, and peace -- the greater good. Yes there are people who skew this belief to benefit them or use religion to wrongly justify bad doings and concepts; but when people truly believes in the true God -- One who created humans with love and dignity, who desires the good of all his children, who built in us a desire for Him -- a good moral basis is formed in the person, the family, the community, and so on. There are people who "believe in God" who do terrible things in His name, but those people don't believe in God, they believe in a false God. One who lives her life for God, lives a life doing the greater good for which God yearns: she does service, treats people with love and respect, pushes for justice in society, and lives a morally-guided life. All these actions are in alignment with the belief in the true good and loving God.
Everyone has different beliefs when it comes to God. Some do not believe at all, while others believe 100 percent. When you place your faith in Him, blessings fall in your lap daily. It is up to you to see them. These blessings help you become a better person, which in turn leads to greater good, whether it be in just in you, or those around you whose lives you touch.
Belief in God can only serve to better society on a whole. If more people had the underlying belief that they were going to be held accountable for their actions on an eternal level, violence in the world would drop to an all-time low. Many people have no fear of the legal system, but may fear eternal torment if they believed in the concept of hell.
You don't believe in God for the greater good. You believe, because it is a spiritual experience between you and the Almighty. Updating the country's infrastructure is serving the greater good. My belief in God helps me. Through Christian teachings, I'm encouraged to think of others and I try to. Still, the belief in God is an individual experience. The term "Greater Good" usually refers to philosophy, ethics, or political science -- NOT religion.
Just look at history. The Crusades, Missionaries, slavery. They had religion as part of what they are. I am no saying led by religion, but religion cultivated ideologies.
Take the US, down south, bible belt. Slavery was huge in the south.
Dont forget, people have morals and ethics without religion. Religion paints a us vs them mentality.
Let go of religion and welcome humanity
There are many examples where people used God and Christianity for their own motives. For example, Crusaders invaded Jerusalem and killed people in the name of God. The Ku Klux Klan also only accepted white Protestants and killed and terrorized people in the name of God. Also, the Church also burned many people as witches or pagans during the dark ages.
There has long been discussion about this very subject. There has been some evidence that people who don't believe in God actually have a lower involvement in crime. I have noticed that my friends who are atheists are much more peace loving and worried about the current health and wellness of people than some who are God-loving. Not to say that these two things are absolutes, but there is absolutely no evidence that belief in God is for the greater good.
If a person wishes to do harm, they will do harm in the name of God if they believe in him. If you want evidence, take your pick of criminals over the course of human history- there are countless of them. If a person truly wishes to do good, they will do good regardless of the presence of God. You meet plenty of secular people who are moral and caring people. And people can find meaning and joy without God, so I really see no reason that such belief is for a greater good.