Glad I didn't bother to read it! I could have predicted exactly what it said. These guys are rarely original thinkers (at least the Unabomber had a slightly different agenda!).
I think you slightly neglect the differences among migrant groups, both beween Hispanics in the US and Muslims in Europe (seems to me that the latter tend to be a bit more socially-conservative) and between different groups within each category (Somalians are different from Bangladeshis, say, the former is, after all, a seriously broken country).
The thing about birth rates is that it's somewhat true. The religious have slightly more children than non-believers, but the big difference is between 'moderates' and hard-core hard-liners. And that applies across almost all religions (look at the rate of growth of ultra-orthodox in Israel or Amish in the US). What's the answer supposed to be, though? 'Genocide', or at best 'build a fortress and try and hide in it and defend it with extreme violence, only to realise you are now locked inside a fortress with a bunch of crazy armed incels?' That's not just profoundly immoral but also unworkable.
And even though I'm an atheist, if the long-term future of humanity is religious, for simple Darwinian reasons, I say, so be it. Ultimately, in sort-of grand cosmic sense, why should I care? If it turns out that is required for people to continue to reproduce, then OK, that's just how it is.
But the sane option is surely to hope that religiosity wears off, that the children of the hard-core religious will always ultimately tend to defect and be seduced by the secular?