This isn't necessarily a good argument given that they have theological objections to birth control.

Given that there's no god to specify what theology you get, this just raises the question — why do they have those theological objections? You're proposing what amounts to a null hypothesis in your notion that "the exact results may be to some extent essentially stochastic".

One example that might prove an interesting contrast in this context to the Christian right outlook is that of Orthodox Judaism.

Or the various cultures wherein are found the murder of women who have extramarital sex and other forms of "honor" violence. The differences do not seem to be described well as theological differences, since some of the same behaviors exist across different religions in some regions of the world.

It is easy for atheists to come to the conclusion that religious people do nasty things because of religion. I suspect that it would be more accurate to say that religion provides a set of powerful rationalizations for certain emotional reactions; and that which reactions a person manifests has as much to do with other elements of culture as with their theology.