I thought someone might pick up on the thread title. I should have worded it differently. Could it be a question a theist might ask...just a thought. It wasn't the intent however.
Back on topic, I think I would need to know if belief in God actually contributes something to our survival. Does faith in a supreme being directing or controlling our destinies tend to make a individuals braver than they really are? By that I mean a foolish courage, a willingness to sacrifice oneself believing full well it isn't the end. Now I realize that there are many reasons other than religious for people to risk their lives. However the thread is not focussed on them right now.
I think whatever we come up with would be very speculative, but I can take a shot - note, I will not form a conclusion....
Pro-religion/Anti-atheism (in terms of survival as a species)
can instill positive forms of individual bravery which might help humans at key junctures - let's imagine we must colonize another planet to survive. Notions of sacrifice and goodness coming from religion might inspire people to acts that save the day.
can cohere groups of people, so that they have sense of being in community with others
can make one assume things and so people assume God has given them a way out of some problem, so they hope where they might not and discover a way to keep the sun from fading out or going nova.
can, Absolutely - in its Abrahamic forms - give humans the right to think the world is their to do with what they will. So perhaps they will save themselves even though this means the destruction of most or all other species.
can give solace in bad periods where there is no logical reason to not succumb to depression.
can give meaning to life and purpose and this might also carry homo sapians through tough periods.
Anti-religion/pro atheism (in terms of survival as a species)
religion can cause division between people and war
religion - certainly some of the big ones - consider 'the world' less important than the afterlife. This can allow destructive behavior and a lack of care and stewardship.
religion can give homo sapians a sense of being more important than other species, species that turn out to be vital for the survival of homo sapians - ecosystems can replace the word species here.
Religions might lead to inaction and expectations of being rescued by a deity.
Relgion might limit options - for example technological - that were considered sinful.
This is just some of the first things that came to my mind. Probably just a start of some full list. I am not even sure I hit the main points.
Religion is so complicated that to ask, which we are basically doing here,
what does religion cause/prevent/make more likely?
is a vast question.