Half Sigma finds that religiosity is correlated with fertility, and nothing else makes much difference. In particular, intelligence makes little difference, except that smart people tend to be less religious by the measure of religiosity used.
His measurement of religiosity is Biblical Literalism, which is more a measurement of which religion one subscribes to, rather than how much one subscribes to religion: Thus, a better conclusion is that some religions encourage fertility, and others discourage it.
A brief wander between religious gatherings reveal that some breed, and some do not, thus chances are that any measure one uses, will correlate or not depending on the extent that high fertility religion happens to correlate with whatever measure of religiosity one is using.
It seems likely that the correct measure is attendance to particular churches and religious organizations, rather than beliefs that do not in themselves directly affect sex and reproduction.
Secondly, fertility correlates negatively with educational attainment, but again, not with intelligence.
But if attainment, but not intelligence, then obviously attainment is the wrong measure: The right measure should be attendance, not attainment. We should treat educational institutions as yet another church or religious organization.
In which case we will find that the religion taught at some institutions discourages fertility, and the religion taught at other institutions encourages fertility. That reform Jews don’t breed, while orthodox Jews and Mormons do breed suggests that the critical variables are hypergamy and patriarchy. To the extent a religion encourages hypergamy, it discourages fertility, and to the extent that it encourages patriarchy, it encourages fertility.
Attendance at educational institutions, viewed as religious attendance, encourages hypergamy. Girls are taught that they are entitled. They can have it all. A girl of average looks can, she is told, have a career and a financially successful faithful lover who looks like Brad Pitt.
Half Sigma’s measure of religiosity tends to favor churches that refrain from encouraging hypergamy. If the question had been “We are children of the universe, and there is a cosmic force that cares for us”, I am pretty sure that religiosity so measured would be negatively correlated with fertility, massively so.