I actually think lack of religion is one of the major reasons for a declining birth rate. The church was an important third space.
Even now in the Korean-American community, the running joke is that if one suddenly starts going to church in their 20s, it's only because they're looking for a romantic partner.
The "Bangladesh Miracle" says otherwise: by intensive effort the birth rate was brought down from 6.7 to 1.89.
(people keep forgetting how much reducing population growth and teenage pregnancy has been an explicit policy goal for decades! Getting it down to replacement rate is good, now we're arguing about the other direction needlessly)
That's because they have arranged marriages, and Muslim women have no choice in the matter. Men don't need to be good at socializing with women to reproduce when women are treated as property.