I think fundamentalism is too brittle to persist like that over the long term.

Yes, the most conservative religions usually have a lot of kids, but over the generations, many of those kids will leave the religion, or at least join a less fundamentalist strain and have fewer kids. Unless the culture is kept strictly separate (increasingly impossible), the quality of life that the surrounding secular culture offers is too alluring. So standards are relaxed, women get educated and start working, have fewer kids. And it ripples down the generations. It hasn't happened yet in some of the less developed parts of the world, but as they get richer, it will. It always does.