I wish I could pin it down. Some Big Think or similar forum talk. They discussed exactly the issue you bring up - the large differential birth rates between the very religious and the secular.
EDIT: Ha! Found it. "Shall the Religious Inherit the Earth?", byt Eric Kaufman
See http://www.amazon.com/Shall-Religious-Inherit-Earth-Twenty-First/dp/1846681448
and youtube talk at the Festival of Dangerous Ideas
https://www.youtube.com/watch?v=IYEyv5a_3LM
The worry is that in 2100 or 2200, if for some reason the singularity hasn't happened, fundamentalist Muslims are a democratic majority in France and evangelicals are a majority in the US, and now there is a far more serious threat than that of ISIS, and the question of whether, with the technology of 2200, the US can disable France's nuclear weapons in a first strike is raised.
I think you're basically correct that in democracies, and even quasi democracies, it doesn't take long for differential birth rates to transform a society, but you are in fact underestimating the effect. The shit will hit the fan long before 2100.
http://www.nationalreview.com/article/361804/russias-demographic-revolution-daniel-pipes
Russia is already approximately 15% muslim, with huge differential birth rates between christians and muslims. And that 15% understates the real issue for violence and control - who has the most young men. I've seen numbers that by 2020 (!) half the Russian army will be muslim, and that majority will only grow from there.
EDIT: Speaking of the shit hitting the fan, there's an article about the potential for Putin to lose power, and what could replace him.
http://www.vox.com/2015/1/5/7482441/how-putin-lose-power
But Navalny certainly seems to have demonstrated racist attitudes in the past. And he could play the "we Russians are being bled and exploited by the people from North Caucasus, by the people from Central Asia" card.
That plays to a depressingly powerful strand of common Russian public opinion, and it's something against which Putin has surprisingly little defense. That could conceivably build a wider public constituency quite quickly if Navalny is willing to play that card.
Putin has been stoking the fires of "the international world is holding us down" for a long time. We are Great and Imperial, but we have been Betrayed. Add the demographic threat to christian ethnic Russians, and they can really get that party started.
In Moscow, Tatar women have six children and Chechen and Ingush women have ten on average.
!
Look at the Ukraine - part of the population identified as Ukrainian, part as Russian, and it lead to a civil war. That was just nationality, this is nationality and religion and ethnicity. Is there going to be a civil war in the world's most heavly-armed nuclear state? Will they start sneaking suitcase nukes out?
Politics is the mind-killer. Politics IS really the mind-killer. Please meditate on this until politics flows over you like butter on hot teflon, and your neurons stops fibrillating and resume their normal operations.
Preface
I've always found silly that LW, one of the best and most focused group of rationalists on the web isn't able to talk evenly about politics. It's true that we are still human, but can't we just make an effort at being calm and level-headed? I think we can. Does gradual exposure works on group, too? Maybe a little bit of effort combined with a little bit of exposure will work as a vaccine.
And maybe tomorrow a beautiful naked valkyrie will bring me to utopia on her flying unicorn...
Anyway, I want to try. Let's see what happens.
Intro
Two recent events has prompted me to make this post: I'm reading "The rise of the Islamic State" by Patrick Coburn, which I think does a good job in presenting fairly the very recent history surrounding ISIS, and the terrorist attack in Tunis by the same group, which resulted in 18 foreigners killed.
I believe that their presence in the region is now definitive: they control an area that is wider than Great Britain, with a population tallying over six millions, not counting the territories controlled by affiliate group like Boko Haram. Their influence is also expanding, and the attack in Tunis shows that this entity is not going to stay confined between the borders of Syria and Iraq.
It may well be the case that in the next ten years or so, this will be an international entity which will bring ideas and mores predating the Middle Age back on the Mediterranean Sea.
A new kind of existential threat
To a mildly rational person, the conflict fueling the rise of the Islamic State, namely the doctrinal differences between Sunni and Shia Islam, is the worst kind of Blue/Green division. A separation that causes hundreds of billions of dollars (read that again) to be wasted trying kill each other. But here it is, and the world must deal with it.
In comparison, Democrats and Republicans are so close that they could be mistaken for Aumann agreeing.
I fear that ISIS is bringing a new kind of existential threat: one where is not the existence of humankind at risks, but the existence of the idea of rationality.
The funny thing is that while people can be extremely irrational, they can still work on technology to discover new things. Fundamentalism has never stopped a country to achieve technological progress: think about the wonderful skyscrapers and green patches in the desert of the Arab Emirates or the nuclear weapons of Pakistan. So it might well be the case that in the future some scientist will start a seed AI believing that Allah will guide it to evolve in the best way. But it also might be that in the future, African, Asian and maybe European (gasp!) rationalists will be hunted down and killed like rats.
It might be the very meme of rationality to be erased from existence.
Questions
I'll close with a bunch of questions, both strictly and loosely related. Mainly, I'm asking you to refrain from proposing a solution. Let's assess the situation first.