> is the least poor and most educated state
I think this is the opposite of a "corrected for X factor" we usually see in studies - this is suggesting that economic situation is a bigger factor in fertility than religious practices.
That should be a "duh", but having more resources resulting in fewer kids is the opposite of the malthusian hypothesis that this is limited by resources/mortality & is driven by personal choice to have kids (and kids do better when parents explicitly choose to have them).
They're saying it is a small factor, not that it does not influence it, because if you correct for economic climate, there are definite differences that you can measure, because personal choice is definitely influenced by how many kids your social circle have.