The alternative to religion is a kind of bleak materialistic atheism leading to despair and depression. Religion brings hope and purpose; its also brings fear of an afterlife or afterdeath which puts things in perspective. If all we believed in was evolution of the strongest then society would break down.
Monotheism is bad for society when you look at Abrahamic religions, they still rage war with each other and still condemn innocent people to eternal damnation unless we get brainwashed in to their particular belief system.
The main objections to religious society, at least Christianity, from my experiences are usually that:
1.) Religion leads to erroneous beliefs on scientific knowledge and is nothing more than superstition.
2.) Religious beliefs inevitably lead to a particularly odious type of intolerance of other people (E.g. Violence).
3.) God is evil and should not be a religious authority for society.
There are other arguments, or arguments that fall somewhat under these umbrella arguments, but that is what I usually come across from my non-Christian friends.
My general response to these ideas are something along the lines that:
1.) Religion and science are trying to answer different questions about what the world is. Science looks at what is observable, but if there was a God who can make themselves hidden or known at will in idiosyncratic ways, then it's hard to come up with an experiment that can observe God, since God is endogenous to the experiment. Science also cannot answer questions on why life is the way it is or how we should change what we should observe.
The old logical positivist movement of the early 1900s (Which the New Atheist movement may be trying to renew in America), doesn't seem sufficient to me in understanding how modern society should be. What ends up happening is a lot of atheists or agnostics shed the supernatural religious beliefs, while still holding onto many religious ethical beliefs (And shedding ones that are unpalatable to them). Secularism has value in preventing government tyranny, but doesn't do very much in terms of giving citizens a moral framework to orient themselves in society. It espouses toleration, but toleration isn't a moral virtue.
What I mean is that toleration is a social contract. I don't have to tolerate a Nazi in my house because they are not tolerant. Toleration is something that we agree to reciprocate, or else we do not continue to associate with a person. Toleration has value and is related to morality, but we don't say it is a moral absolute. This is one way I think about the shortcomings of secularism in guiding morality, though I don't know if I've made my point clearly. I'd have to commit a lot more time to its discussion.
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2.) Religious beliefs are often used to justify violence, or at least ridicule of those with different beliefs. Some people believe that without religion, people would be much more rational on the whole compared to what we have historically seen. Yet historically, most people were religious, and if you're a powerful ruler, you have a great capacity for violence. Naturally, most violence we observe historically will be by some religious person. Yet without religion, an evil person would find another reason to be evil. There doesn't have to be a good reason to be cruel or odious to other people. People are just evil.
Religion has both the capacity for great evil and great good. Whatever has institutional power and authority will have great capacity for evil. What was the model that Christ gave us? That he would use authority and use it to serve us, even to the point of death. It is under this model that Christians can use power and authority for good. I am not saying that religion requires cultural or even political hegemony for good. Theocracy didn't work for Israel, and neither did the monarchs and their "Divine right". Rather, religion can provide us a moral framework for service to others and great acts of self-sacrificial love for others. Even if society--religious or secular--is doomed to their own vices as a whole and needs to be periodically rebuked, individuals can provide great services to society.
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3.) Responding to this would require a whole post of its own. From the Christian perspective I have, God spends a lot of time in the Old Testament showing that people are unable to redeem themselves. Even if God sets a very low bar for laws and ethics (E.g. God allows slavery in the Old Testament) and tries to slowly shape a society over time, say, through a chosen people and the promise of greater reward if the nation is righteous, society is doomed to become wicked. I don't think God showing this off is particularly evil, that God allows for evil rather than hold back the hand of every sinner and turn everyone into an automaton that can do no wrong. I will leave things at that for now.
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Perhaps really, even after all this, it is not religion per se that will be good for society. Nations will generally place their sovereignty above that of any human rights when push comes to shove, and societies will act selfishly at the local or national level. It is really that we wish for something majestic and greater than us that we can be personally connected to, that we can be cared for and given a reason to die. Therein is a great value of religion, even if you are non-religious and are an outsider looking in.
An individual living in a materialistic society might think they are relegated to existential dread of dying without justice, with nothing after death, in exchange for political and sexual liberation. But I think it is plausible, and much more freeing, to believe in a life where there will be a judge, and we do not have to take on that task ourselves of judging others or taking vengeance for ourselves, which we may very well be powerless to do in greater society. We can simply live knowing we are loved, that we will have a reason to die, and then die peacefully. That's the gist of how I'd argue anyhow.