It not religion per se that's becoming extinct in these nations, it's just some form of Christianity (usually, a very moderate and modernizing form). Detailed demographical studies show that fundamentalist religion (e.g. born again evangelicals and devout Muslims) is definitely on the rise, and associated with by far the largest fertility rates.
In addition, I think it's misleading to count "no affiliation" as "no religious beliefs."
What about new-age spirituality, alternative spirituality, etc.? Those typically don't show up in these kinds of studies, but they do qualify as religious beliefs.
Detailed demographical studies show that fundamentalist religion (e.g. born again evangelicals and devout Muslims) is definitely on the rise, and associated with by far the largest fertility rates.
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