Current examples are the rapid growth of Orthodox Jews as a percentage of Israel’s population, and evangelical birth rates in the US.
My bet is that given technology to allow massive extension of fertility into older age, the fertility differences between religious groups that believe in a religious duty to procreate, and everyone else, will increase even more.
I like to joke that the Amish are obviously the one true religion because eventually they'll cover the earth: They live long and peaceful lives, have scores of children, and are among the best farmers on Earth.
As long as the rest of us don't do something horrible the end state is inevitable.