This doesn't seem to track with broader sociological trends. For example, let's compare the USA, one of the most religious Western countries, with the USSR, whe

This doesn't seem to track with broader sociological trends. For example, let's compare the USA, one of the most religious Western countries, with the USSR, where 60%+ of the population was atheistic, and where the state promoted atheism. Between 1960 and 1980, the US population grew from 179M to 226M (a 26% increase). The USSR population grew from 208M to 262M (a 25% increase). So, despite massive differences in religiosity, the population rate was pretty similar. China, another largely atheistic state, grew from 582M to 1B in roughly the same period - a 73% increase. So while it may be true that certain small deeply religious populations are more incentivized to have children, this doesn't seem like a significant effect at population levels overall. You'll also find small non-religious groups with similar behaviors.