I have known lots of people who have or have had large families who were not what I would call "very religious." For example, lots of C&E Roman Catholics. I have known a few very religious people who had large families but I don't know any now. I imagine the best place to look would be Africa, the Middle East or Utah.

I have never known a-religious or atheists or even agnostics who had very large families. I'll arbitrarily stipulate that "very large" is more than five living children from the same marriage.

For example, I came from a family of 6 surviving children from one marriage. My Mother is quite religious while my Father was a wishy-washy atheist. So in my case, a partial exception, my Mother's religious leanings may have had an influence more than my Father's. My Mother's family (C of E) ran to small families even back through the 19th century. They were urban, merchant and working class. My Father's family was Presbyterian or Baptist and ran to huge families for generations. They were farmers and ranchers and religion was a very important part of their lives.

In the area where I live Roman Catholicism is the largest single sect, though the majority of people are not Roman Catholic. One of my co-workers, probably an atheist (we don't talk religion at work, but he's a biologist and most biologists are atheist or atheistic-agnostic) is from a Roman Catholic family. He has 9 living siblings from the same marriage. Both of his parents came from families of greater than 6 living kids. This is not uncommon for my generation in this area. But few if any of my generation, regardless of religious leanings, have more than 3-4 kids. Most have 1-3.

What does it all mean? I don't know. My inclination is to blame shrinking family size on increased education and voluntary, simple birth control. Also, religion is generally less integrated into their lives than it was with my grandparents, especially the country cousins whose social life revolved around the church.