Another is the rapid rise of new denominations. In the 19th century Methodists and Baptists -- Finke and Stark call them "the upstart Protestants" -- outnumbered previously more numerous Anglicans, Congregationalists and Presbyterians.
The Catholic Church grew not only among previously Catholic immigrants but also by making converts. Black Americans formed their own churches, which have thrived to this day.
The Church of Jesus Christ of Latter-day Saints and the Assemblies of God, both American creations, have attracted millions of followers here and around the world.
The 20th century saw the rise of evangelical and Pentecostal churches. Recent decades have seen huge rises in membership among such churches and continuing decline in the rolls of mainline Protestant denominations.
Surveying this history, Finke and Stark conclude that "religious organizations can thrive only to the extent that they have a theology that can comfort souls and motivate sacrifice."
Churches that make strong demands, in doctrine and in service, tend to grow. Churches that water down doctrine tend to decline.
"Theological refinement," Finke and Stark write, speaking of watered-down faiths, "results in organizational bankruptcy."
It should not be hard to understand why this is so. Many people seek structure and community. A church that makes strong demands and requires strong commitment can provide them.
Harvard sociologist Robert Putnam notes that churchgoers have more social connectedness in their communities. American Enterprise Institute President Arthur Brooks shows that religious people contribute far more, in time as well as money, to charity.
The journalists advising the Catholic cardinals, some of them former Catholics, think a church that is closer to secularism will attract people like them.
But in a country that doesn't penalize nonbelievers and imposes little stigma on them, the easier alternative is to stay home on Sunday or go out for brunch.
I'll watch with interest as the cardinals choose a new pope -- who, I suspect, will not be looking for my advice.