I must say, following the migrant crisis is most stimulating. But just for clarity's sake, I want to draw a few lines.
I am definitely not a believer in the silly thesis of Eurabia, or, to quote the title of Thilo Sarrazin's 2010 book, that Germany is 'doing away with itself' ('Deutschland schafft sich ab'). It's also silly to talk about the 'Islamization' of Europe.
Germany is not destroying itself and will never be Islamized. There are 4 million Muslims living in Germany right now, and most are, of course, productive, law-abiding citizens. Residents of German with non-German roots have in aggregate lower incomes and less education than ethnic Germans. They are also disproportionately likely to commit crimes and live on social welfare benefits. But the vast majority don't do these things, of course. And the social deficits of 'Muslims' as a whole mask huge differences within the German Muslim population. The principal reason for these somewhat disappointing numbers are Germany's 2.2 million Turks, who do much worse than Germans on almost every measure of social adjustment. Other Muslim subgroups do better than ethnic Germans.
Even the incorporation of 3 million new mostly-Muslim migrants won't change this state of affairs much. We're just beginning to get information about the migrants coming in now. The consensus seems to be that about 20% have college degrees, and the average level of education seems to be about 6th grade. Assuming they stay, about 30% will probably be able to learn fluent German, and another 30% will learn acceptable German. The top 20-30% in terms of cognitive ability and education — the engineers, lawyers, doctors, accountants, nurses, teachers, pharmacists, dentists, etc. — will adapt successfully to life in Germany. They may not be able to practice their former profession, but they'll find work and integrate easily.
The next-lower 30-40% will get some sort of work, possibly after a very long delay. They'll find work in areas in which a limited knowledge of German isn't a problem. Warehouse worker, tailor, cashier, butchers' or bakers' assistant, mover, electrician, nurses' aide, home healthcare worker, helper in a family-run shop or waiter in a family-run restaurant, Uber driver, park groundskeeper, janitor, etc. The kind of thing that immigrants do now in Germany.
The least-qualified 30-40% will live off social welfare benefits and odd jobs. They won't ever learn more than a rudimentary vocabulary of 500-1000 words, and will be disproportionately likely to commit crimes.
The Magic Pixie Dust crowd wants us to see all the new migrants as a wonderful opportunity. They will immediately start inventing fabulous new products, obediently work themselves stiff, teach Germans how to love again, and fill our neighborhoods with nothing but Vibrant Diversity™. The doomsayers say they'll never find jobs, they'll all turn into criminals, they'll carry out terrorist attacks, live off social welfare benefits for generations after generation, and drag Germany down into poverty and mediocrity.
Neither the Magic Pixie Dust crowd nor the doomsayers are right, if you ask me. The current crop of migrants will have hugely diverse experiences. Some will turn out successful, others,. as I have argued, will greatly increase the scale of existing social problems in German inner cities. I think this is not a good policy outcome, which is why I have been highlighting the very real problems migrants will bring with them. But none of these problems will come within light-years of destabilizing German or any other European society. All West European countries currently have severe social problem in their inner cities, and most have much worse problems than Germany. At no point have these social problems come anywhere near close to threatening the overall stability or prosperity of these countries. And they never will. The numbers just aren't there, and never will be.
And as for Islamization, this is also a chimera. The new immigrants are also going to have a huge variety of approaches to Islam, from fervent fundamentalism to a totally secular viewpoint. Most of the women wear headscarves, but I know from experience that you can't tell anything merely from this practice. So they'll build more mosques in Germany. So what? Doesn't bother me. More than 9 out of 10 Germans will still not be Muslim. The number of Germans who convert to Islam will continue being infinitesimally small. Contemporary Germans are simply not interested in any traditional religion of any flavor, except perhaps Buddhism.
As for undermining 'German values', this is also a silly nebulous fear. How can a country in which the most popular movie in recent years was called 'Fuck You, Goethe!' (misspelled in German!) claim that the masses are still nourished by the elegance of Weimar classicism? As is the case all over the world, Minecraft and Apple will be a thousand times more culturally influential on the average German, whatever their religion, than supposed 'traditional' German values which are kept alive only among aging cohorts of the educated bourgeoisie.
And no, Muslims are not going to take over Europe. Muslim families will probably continue being somewhat larger, but only for a few generations. And as for the notion of millions of Muslims totally swamping Europe, that is not going to happen. As foolish as I find current EU/German policy, the notion that Europe would actually admit massive flows of tens or hundreds of millions of Muslims is just silly. As we have seen recently, European governments can be moved to swift action once they (belatedly) realize the scope of the crisis. There are still open-borders dreamers in the ivory tower, but in the current political climate, they are being totally ignored.