I’ll try to do it justice.
The answer is yes, that it’s correlative. Empirically, yes in the aggregate atheists have fewer children. And yes, its partly causal.
1) Reproduction is losing it’s economic utility as a guarantee of old age security.
2) Consumer capitalism raises the cost of creating ‘middle class and working class children’ and so birth rates decline along with industrialization.
3) Atheism is highly correlative with education, and education correlative with income, and income correlative with decreased reproduction. (Children are a net negative on career development because they are time consuming. Or conversely, careerism in two income household deprives both individuals of the time necessary for child rearing. )
4) Prettier women have more children, married women have more children, women who stay at home have more children. Less attractive women have fewer children. Unmarried women have fewer children. Women who work have fewer children. This is all just data. We have put women into the work force and decreased their rate of breeding RELATIVE to the rates of breeding in other civilizations. (This was most evident in russian and japan, both of whom are facing serious long term economic problems because of it. You cannot easily have both the employment of women AND paid retirement and health care. At least, that’s what it looks like.)
5) With the advent of redistribution, loss of male property rights, and child support and financial support, Women are “marrying the state”, or “marrying the state via child support”. Both of these do statistically decrease reproduction, as they also render the males economically not viable for other women. (That’s the data. Sorry if it’s unpleasant.)
6) The lower classes are dramatically shifting out of monogamy into serial monogamy. Humans are naturally serially monogamous in tribal life. Monogamy is economically competitive, but not natural to man – we evolved to manage relationships that last on the order of four years – long enough for a child to walk with a migrating tribe. The moral prescription for monogamy, and therefor for higher reproduction rates associated with monogamy, was caused by (a) the agrarian mode of production and the family farming unit (b) the politically dangerous problem of single men unable to have access to sex – the source of most revolutions. Monogamy was imposed by religious leadership for these reasons – although we are still trying I think to link all that history together. It looks like it’s a natural evolution, not just the copying of an idea worldwide.
1) The strain on the rest of the planet’s biomass by our enormous population is pretty severe. It’s possible we’re more than twice the population that the planet can handle. We do not need more people. There are no pollution problems. There are few resource problems. There is a population problem.
2) We have created an economic and political system of intergenerational redistribution that requires constant growth and constant new generations.
3) Consumer capitalism seems to put a cap on uncontrolled population expansion.
So it isn’t clear that we need to increase population. In fact, just the opposite. And we could do so, but our current system of redistribution is a system of dependencies that we can’t likely get out of without a political crisis.
So the glass is half full (declining population) and half empty (we are dependent upon population growth that the earth cannot sustain, and which causes political infighting.).
In these cases Atheism is correlative with lower reproduction in the upper classes, and CAUSAL with reproduction in the lower classes.
I hope this makes sense.