Perhaps in a country with a homogeneous religious culture it’s easy to dictate dogmatism, and while the US might be religious compared to perhaps Europe, it is not homogeneous. I’d argue that you could take two different congregations affiliated with the same denomination and probably find topics or scripture that would create fierce debate between the two.
Birth control might be a big deal to some devout Catholics and some primitive/fundamentalist Baptists, but virtually every other denomination and congregation is literally not going to care.
Among religious persons and societies, doctrinal considerations outweigh all others. If you are under the impression that the abortion issue is different because large numbers of non-religious folk are sufficiently motivated by the ethical issue to engage in activism and donate funding, I think you're quite mistaken.