A recent USA Today editorial (here for as long as Yahoonews keeps it up) draws a connection between a decline in European religious faith and a decline in European birthrates. Hmm. Certainly both have been on the decline, but how direct is the connection? The article makes an obvious connection between the decline in religion and the increase in things like abortion, birth control, gay marriage and a general rejection of traditional families. That's not totally out to lunch, but it is very conservative Catholic (and the author acnowledges being a staunch Catholic.) Here in the States we're majority Protestant and we have loads of abortion and birth control. We've also got lots of babies.
The author also worries that secularism in America suggests that we may go the increasingly secular way of Europe. Not in this part of the country we won't! I think it's important to note that "Secularism" in the States is kind of a contextual thing. A lot of European secularism is coming from indifference or hostility towards religion, but many devout people in the States are in favor of ousting the Judge Roy Moores of the world from positions of political influence, not out of hostility towards religion but out of hostility to using the government as a bully pulpit for a specific theological point of view. Oh, and a desire to protect the interests of cultural minorities. On the other hand, something like France's recent ban on the wearing of religious signifiers in schools, including head coverings that are mandatory for some Muslims, was clearly done out of hostility to cultural minorities and to religious practice. But unabashed hostility to religion isn't likely to get very far around here. Flannery O'Connor, herself a devout Catholic and a southerner, saw that the religious threat in the Southeastern US wasn't a decline in religion but a perversion of it.
I suspect economics plays an important role in declining European birthrates. I know a few Swedish people who've expressed sincere confusion as to why anyone would want to get married. Maybe when a country uses socialist collectivism to create a really secure social safety net and dependable health care then people are less likely to feel the need to band together in more traditional ways, like nuclear families.