What is the function of religion?

[Hegel]

Belonging to a minority religious belief is apt to subject you to a lot of extra stress, if not outright abuse and persecution. So, yeah, not being a persecuted minority will probably lead to you being happier. That doesn't suggest that the majority belief system is useful in any way, just that it is good at keeping everybody else down.

You're probably right, but I think there are other factors as well and that is not the whole picture. Perhaps in some US states atheists are well, not persecuted, but regarded with suspicion. Yet, this is no universal condition. Think European countries. I admit that I have no stats, but I guess the patter can be found also in places like Sweden. (disclaimer: atheists are certainly not deemed with suspicion in Sweden, France, etc)

It's easier to be happy and live on the straight and narrow when you belong to the dominant belief system.

Perhaps it is also the case that it is easier to be straight and narrow when you have a belief system which gives you a rigid code of ethics which you must follow in order not to be punished after death and to get your place in paradise?

Population growth is a huge problem, precisely because there are too many people.

Certainly. And here is the catch: when you have two tribes, A and B, and A produces more children than what B does, which one will become dominant and spread its moral code?

So, it is obvious why religions tell you to reproduce.
But in a secular society with effective contraception methods, an opposite problem occurs: people began to produce to few children.

What benefit does religion actually have? Historically, religion has not tried to supplement society, but rather has tried to conquer and define society. What practical need do we have for religion that a technologically-advanced society can't better serve in other ways? I honestly can't think of any.

You are correct when talking about modern history. But one should take a wider perspective. Actually, the phenomenon that stata and church are separate is particularly Western, Christian and modern phenomenon. Evidence is clear:
Rome: Roman state religion with worship of the Emperor (rememver, Christians were persecuted only because they did not take part in it);
China: Confucianism;
Islamic Empire = Islam;
Egypt: Egyptian religion;
Aztec: all the stuff with human sacrifices;
etc.
In other words: the normal condition is not secular, but religious state, that religion and state are one.
So, where does the idea of secularism come from?
This is something most atheists have hard time getting: it comes from Christianity: "give unto Caesar what belongs to Caesar"
There it is, idea of secularism. And it was in reformation (for Catholicism did not quite follow this idea, although it never managed to become a church-state) when this idea was first put into practice full force for the first time in human history. That is to say: it is the very Calvinist sects that most American fundamentalism stems from that were, in reality, the ones that were the founders of modern secularism, freedom of religion, etc.
Irony?
You ask what benefit religion has. Well, in historical perspective you can tell, that secularism itself has religious origins, and if you are are secular, at least you should thank Christianity for making it possible.

For our day ... Well, if you don't have religion, you should have a substitute for its benefits, how it offers meaning for life, offers clear moral codes for ordinary folks, methods to attain some spiritual experience, etc, things which, as some have said in this thread, is what explains why people find religion so appealing. So, the question is not perhaps not so much "why religion?" but rather "what instead of it?" I guess that was what I was aiming at with the opening of this thread, particularly with the last question which was not necessarily put as well as it could have been put. What most secularist offers is simply this: freedom and being kind to others. Now, I haven nothing against freedom nor being kind to others, but I cannot but doubt that this might not be quite sufficient answer to the question.