Extrapolating from the current situation, feminists, liberals, environmentalists and the highly educated don't have kids, while conservatives and religions people do. In the unlikely case that there is no singularity or genetic engineering or brave new world style babies in tubes for the next few hundred years, the world turns back into a medieval theocracy, with nukes.

This is a commonly-repeated point which I have seen no evidence for. Specifically, I am aware of no evidence that propensity to believe in religion is passed on as a hereditary trait. Indeed, there are many human behaviours that would seem to be highly selected against in evolutionary terms but still persist to a high degree in the population (homosexuality, etc.) The reason of course is that these behaviours have a strong developmental component that is independent of genetics.

As an anecdotal example, I am the child of very religious parents and I have zero belief in religion, and I have always had zero belief in it ever since I remember.

People always make the implicit assumption that children are going to be identical to their parents. In practice, culture, environment, and other factors play a huge role. The key to securing the future success of a society lies less in getting 'smart' people to breed and more in providing a good and intellectually stimulating environment for future children to grow up in.