In general what you say is true, but there are some exceptions. The Hasidic Jews are one of the most fertile groups in the US, and they are low income, highly religious, but urban (most of them live in New York City).

You might think they're an insignificantly small group, but the counterintuitively fast nature of exponential population growth means that they'll become surprisingly large surprisingly quickly. They're culturally immune to the influences that caused fertility to collapse in others and they're unlikely to voluntary limit their fertility.