There’s a major problem with this question, and that is that religion is not defined. It’s really tricky, because as someone said above, not too long ago, there was no difference between secular life and religious life.
Nowadays religion can include many features (a deity, an organization, dogma, holy texts, mysticism, altered states of concioiusness, quiet sitting or kneeling, ritual, dance, music, discussions, schools, shelters, farms, industries, and on and on). However, a religion need not have all these things. For example, Buddhism doesn’t have a deity.
Similarly, there are many organizations that have many of these attributes, but are not called religions. Most nations, for example.
In many countries there is an official religion. In many communities around the world, you can’t do any aspect of life without a religious official of some kind there. This is common with agrarian cultures.
So, if we had no religion, we might as well have no people. To make this question useful, you’d have to ask about what life would be like if there were no music, or no meditation, or, and I suppose this is probably what you had in mind, no concept of a Christian God.
I believe that the development of science required the development of the capability of making hypotheses. God is merely a hypothesis. It applies to everything we don’t know. Check it out, yourself, if you believe in a God. When you don’t know the whys and wherefores of something, don’t you revert to “it’s God’s will?”
Yet, as science develops more and more theories that the evidence supports, there is less that we don’t know (although the amount we don’t know will always dwarf what we do know. In any case, God is the explanation for what we don’t know, whereas science explains what we do know.
If we didn’t call that all-purpose hypothesis God, we’d call it something else. It is necessary, because evolution has made humans very uncomfortable with not-knowing. Just think how you feel when you don’t understand why something is happening? You need to try to control it, and yet you can’t, because you have scientific knowledge.
In our minds, this discomfort of not understanding builds and builds and it would drive us crazy if we didn’t develop a way to cope. How about an all-powerful, that shares many human traits (so we can feel it is possible to know it), and controls everything. Hey, if we pray properly, and make the proper sacrifices, this Charater will send us luck, and get us out of trouble.
And if we don’t get out of trouble, it must be our own fault for not being as good as this Entity wants us to be. See? It’s magic! It’s a kind of circular thinking that externalizes our anxiety, and makes it possible to fool ourselves into believing we understand enough about the world.
It is necessary to do this for most people. Everyone finds some technique for dealing with the unknown and the apparant unknowable. For most it is that which they grew up with.
I grew up with no religious training. No church. No dogma. No rituals. My Sundays were free for other things. But, I also missed out on youth groups, and trips, and charitable efforts.
Still, I’ve stuck with what I was raised with. I have nothing to explain the unknown. Nothing to make me feel like I will survive, except knowledge. And the things I don’t know about? Well, I figure it’s ok not to know. In fact, it’s fun. Because it gives me or other scientists something to try to understand.