And while Mormon's rapid breeding might prevent demographic malaise, the rapid breeding of low conscientiousness people won't - the very trait that causes them to breed rapidly also causes them to be generally unproductive.
Birthrates are falling rapidly around the world, yes, including in places you may think are populated with "low conscious" people. The reason is very prosaic: urbanization. As people get crammed into smaller areas, they naturally start to reproduce less.
It goes back to the fundamental human urge to take care of our offspring: an overcrowded city is also a highly competitive city (Tokyo, Hong Kong, New York etc illustrate this best) so people who live in that environment that don't want to bring more offspring into the world.
Even in a country like India, the population growth is almost all rural. The birth rate of city-natives in big cities has dropped well below replacement level, and cities are gaining population because of immigration and within one generation those rural-turned-city-dwellers have low birth rate.
If population A (e.g. mormons, people of low conscientiousness) has a birthrate of X, and B (everyone else) has a birthrate of Y, with X > Y, then population A will eventually become the entire population. The eventual birthrate will be X.
Even if both birthrates are reduced by some exogenous factor K (e.g. urbanization, reducing from X -> K x X, Y -> K x Y), this fact doesn't change.
One way to think of this is that, instead of the physical birth rate of people with the trait, what is the rate with which the trait manages to reproduce itself? A trait of "being Mormon" with an average of 6 kids, of whom 2 become Mormon, leads to a Mormon population of stable size, forever having 6 kids per couple.
If the Mormons manage an average of 2.5 Mormon kids per couple, then their population will grow without bound, though they may never be an actual majority of the population. However history shows that culture is malleable. They may grow that fast now, but a rapid social change can destroy the dynamic. (Witness Italy and Ireland, both strongly Catholic, with declining populations.)
Now contrast this with, say, a genetic trait that manifests as a strong desire to actually have children. Eventually you get a population of people who really want children, most of whose children really want children. This type of fundamental desire is more stable than a social construct.
I believe that there are such traits out there in the population. They are much more strongly favored today than in the past. Eventually those traits, whatever they are, will become more widespread, and evolution will have happened.
Great-great-grandparent:
> Secular culture has managed to peel away many of their kids in recent decades but [...] that process is about to change
However I, personally, see no sign of that process changing. Popular culture does not have to be good to pull away the children of religious people. It merely has to be attractive. And popular culture is constantly, relentlessly, optimizing for shallow attractiveness.
For some bizarre reason, Irish people love having babies.
Full disclosure: I am a childless Irish male in my older 30's, I know many people I grew up who have had kids since the economy went into the crapper.
I personally suspect that the long oppression of the Catholic Church under English rule lead to a cementing of how important it is to the Irish people. I further suspect that, in time, Ireland will become as secular as other countries. But that time is not yet here.