That's realy inaccurate. If anything the more religious you are the more offsprings you have. Atheist societies are below replacement levels. What makes you think fact based thinking leads to more children making?
a lot of weight has to be given to 'what works' - what things grind up against the machinery of reality and survive over the long term? there is a 'truth' to such things
I'll happily admit I'm wrong though, in light of evidence before me
OP is absolutely correct of course. "Show me the money" is the only durable way.
With the usual caveat that "evolution can remain irrational longer than you can stay alive", so no guarantees on the individual level over a single human lifespan.