I’m not convinced. It does that for a high percentage of the population. However, after a period, the smaller percentage of the population that don’t reduce their birth rate will become increasingly dominant.

Current examples are the rapid growth of Orthodox Jews as a percentage of Israel’s population, and evangelical birth rates in the US.

My bet is that given technology to allow massive extension of fertility into older age, the fertility differences between religious groups that believe in a religious duty to procreate, and everyone else, will increase even more.