It's a little more complicated than that: not all religious groups consider all forms of birth control to be sinful, and these trends don't apply in all countries. Increased religiosity won't necessarily increase the birth rate.

Disclosure: my mum, Marion Burkimsher, is a demographic researcher specialising in this area. She's also studied fertility of migrants (the TFR statistics are skewed).

https://www.researchgate.net/profile/Marion_Burkimsher/publi...