The Idiocracy theory. The trouble is that the traits behind the birthrate differences you're observing aren't genetic but financial: it's not genetically "dumb" people who have more kids, it's poor people, and genetic lines that transition out of poverty generally see commensurate birthrate drops.

If poor people were going to "outcompete" and wipe out rich people, it would have happened a long time ago.

Also, "religious" have been steadily declining for a while, so that theory doesn't work out. (Of course, the idea that most bad behavior stems from religion, and everyone would be nice to each other without it, is another fallacy.)