You're neglecting a different factor that is more highly (and negatively) correlated with fertility than religiosity: level of education in mothers. Religious families significantly outreproduce nonreligious ones only where their level of education is also significantly lower. (Quiverfulls homeschool, ultra-orthodox jews in Israel have their own schools, muslims in Europe and Russia tend to live in poor areas with comparatively bad schools.) Of course these two factors are causally linked: lots of religions have explicit or implicit norms against girls' education. But to neglect the stronger one of the two is to mistakenly see an unassailable problem.