Congressmen don't believe in evolution, ergo natural selection is a lie because of jesus. On the plus side, natural selection will kick in for humans as well when getting infections removes you from the gene pool, thus making humans more naturally resistant to infection.
A lot of religious folks, who do not believe in natural science, are procreating much more(and at an earlier age) than the average population. With this in mind, I don't think natural selection will be beneficial for civilization...
If it were impossible for the children of anti-science fundamentalists to constitute a sufficient and sane majority to protect science, we'd have almost certainly never gotten to where we are.
That America, a country populated largely by those whose primary intent was the pursuit of religious fundamentalism, was ever the world lead in science and technology puts rather large holes in the "fundamentalists breeding will be the downfall of us all" argument.
Similarly goes the concern about "dumb people breeding more/faster" necessarily leading to the dystopic future of IDIOCRACY.
We can absolutely suffer a reversion to fundamentalism and/or a rise of proudly celebrated ignorance. There are plenty of historical examples of civilizations falling to those threats. I'm just saying that we also have plenty of data that it needn't necessarily go that way.
There's no large scale correlation between religion and procreation. On the other hand, there's a good correlation with wealth/living standards; namely, richer countries reproduce less, poorer countries reproduce more.
Most religious people (in the USA) believe in "micro-evolution" but not "macro-evolution" (both terms have been made up by religious people).
They accept that evolution can cause variations within species (anti-biotic resistant bacteria being a very clear example) but don't accept that evolution causes speciation.