A study which also attempted to model societies that weren't trending towards religious extinction be a lot more useful (the states were most likely chosen for readily available data rather than being selected due to being exceptional in their levels of religious disaffiliation). Right now I'm seeing a correlation between "nations which make detailed census data available in convenient form to academic researchers" and increasing levels of religious disaffiliation and low birth rates.

The same model would probably fit quite well to countries where there's a marked trend increase in a specific religious affiliation, like Indonesia where dominant and growing Islam may hypothetically be decades away from making other affiliations extinct. Does Indonesia have a correspondingly much higher fertility rate? Actually no (~2.28), especially not if you control for other variables like poverty and infant mortality that are known to be correlated with high fertility rates. And it's dropping.