> Also the groups that have many kids (the Amish have 7 children on average, and you also have Mormons and Orthodox Jews) will expand exponentially
I agree with your overall point, and about the Amish and Orthodox Jews (especially the ultra-Orthodox, Hasidic/Haredi).
However, for Mormons, I'm not sure that is true. Mormons, in the US at least, have plummeting fertility rates, and also a lot of problems with retaining their younger members. They don't belong to the same category as Amish and ultra-Orthodox do, they are converging to the American secular mainstream while those groups remain on a clearly different trajectory from it.
When I say "Amish" I mean "Old Order Amish". Mennonites have both lower fertility and lower retention, so their demographic future is less bright overall.
That said, there is a subgroup of the Mennonites, the Old Order Mennonites, who have fertility and retention much closer to that of the Old Order Amish. The Wenger Mennonites, in particular, are rather similar in those measures. But only around a third of Old Order Mennonites are Wenger, and only around 15% of Mennonites in the US are Old Order.
Something affecting Mormon fertility rates specifically is the dramatic increase in housing costs in the “Mormon Corridor” (the inter mountain us west strip of geography where most Mormons live). It’s simply too expensive for most young Mormon families to live the lifestyle they used to; with large homes and large families.
That area of the US has some of the most newly unaffordable areas in the country
It’s also possible that secular society creates effective off-ramps to convert the hyper-religious to secular values. I’m uncertain if this will work given how successful the in-group remains despite the internet and modern social media.
Many ultra-Orthodox Jews use "Kosher Internet filters" – filters that block content that isn't approved by their rabbis. In Israel, you can buy "Kosher phones" which have this software pre-installed by the telco and locked down so you can't remove it.
People assume that technology necessarily encourages secularism, but it doesn't inevitably do so. Technology also makes possible new methods of social control which can be used to suppress secularism.
I agree with your overall point, and about the Amish and Orthodox Jews (especially the ultra-Orthodox, Hasidic/Haredi).
However, for Mormons, I'm not sure that is true. Mormons, in the US at least, have plummeting fertility rates, and also a lot of problems with retaining their younger members. They don't belong to the same category as Amish and ultra-Orthodox do, they are converging to the American secular mainstream while those groups remain on a clearly different trajectory from it.