Well, atheists in advanced technological societies have half the birthrate of the religious. That's a simply enormous difference in fertility and cannot be ignored! Part of that is the enthusiasm with which atheists embrace the behavior values of the sexual revolution, which is strongly negatively correlated with live births.
So what I expect to happen is a drastic decline in atheism as atheistic subcultures remove themselves from the gene pool through memes like "childfree", "antinatalism", "right to suicide" and the like.
I wish you were joking, but apparently you are not. We've been entangled in this discussion before, but it bears repeating:
Overpopulation is the reason behind almost every aspect of the most daunting environmental disasters in existence, and will most likely be the cause that kills us all eventually.
Huge families were necessary in the past, when less than half of your children were likely to reach adulthood and producing as much offspring as possible was your best chance of actually having an heir to carry on your traditions. But with the advent of modern medicine, all of that changed, and mankind exploded like a swarm of locusts - with similarly disastrous consequences for everyone involved.
Oh, sure, perhaps we might struggle on a little longer than those mindless insects, turning the collapsing ecosphere into a prosthesis for our own survival, squeezing out a bit more nourishment before the catastrophe catches up with us. But an ever-increasing species (or even one that remains at current population levels indefinitely) will as surely die as the aforementioned locust swarm.
I consider it positively IMMORAL to have more than two children. I have heard people defend their selfishness by pointing to the fact that most of the population growth takes place in developing countries, and populations are shrinking in "the West". But how does that negate the fact that they are nonetheless contributing to a global population growth that will destroy us all, and thousands of other species along with us?
Coming back to your original observation about religious conservatives "outbreeding" non-theistic progressives: this presupposes that these children will grow up to share their parents' views, but more often than not, that is not the case. Especially not in a society where a free exchange of ideas and a wide range of information on other world views is still possible.