There are several Catholic countries that have lower birth rates than the US. The thing that most of them have in common is that they are developed countries. Mainland China, an atheist country, has a higher birth rate than several Catholic countries. Mainland China is a developing country, while the Catholic countries that have lower birth rates than it are developed countries.

This supports what I am saying, which is that religion doesn't determine whether or not a country or a population will have a low or a high birth rate. What determines it is the economic environment of a given population and how well educated the women in that population are (this is backed up by studies as well).