do either of those have to do with 'secular, socially conservative society' part?And then birth control happened.
Worse, for the last few decades, birth control was mandatory.
There's no going back to the before times.
non-secular societies:
Iran: birth rates collapsed in the 2000's, despite not being anywhere near secular.
Saudi Arabia: birth rates collapsed in the 2000's, also despite not being anywhere near secular.
non-conservative societies:
Finland: birth rates collapsed as early as 1972, despite not being anywhere near socially conservative.
Ireland: birth rates collapsed in the 1990's, despite not being anywhere near socially conservative.
There are no religious yet socially liberal societies in existence as a comparison, so I can only do single counterexamples.
So, what countries have high birth rates?
Poor agricultural and mining ones with low GDP, literacy and life expectancy.