A specter is haunting Europe
There are differences, of course. Islam is far more ideologically intractable; the content of its core beliefs renders it inherently more prone to violence and far less capable of compromise with secular society. Also, the Muslims in western Europe are almost entirely recent immigrants or descendants thereof; western Europe, far more culturally secular than the US, imported this completely unnecessary problem starting in the 1960s. Opposi- tion to further immigration from Muslim countries has become a major issue pitting western European populations against their pro-immigration ruling political elites.
The most alarming and widely-repeated claim about the Islamic threat in western Europe, however, is that Muslims are likely to overwhelm the native Europeans demographically and Islamize their countries. Is this plausible?
To begin with, the Muslim population in western Europe is quite small, less than 5% of the total in most countries. France has by far the largest Muslim minority, both absolutely and relative to its total population; it is generally estimated at five million, which would make up only 8% of the total. Higher percentages are often cited, but these refer to a few major cities in which Muslims are concentrated. Similarly, figures like fifty million are sometimes given for the total Muslim population of "Europe", but the only way such numbers can possibly be arrived at is by including places like Albania and northwestern Turkey which are technically part of the European land-mass but have been majority-Muslim for centuries, as well as the "Muslim" population of Russia (most of which isn't actually Muslim). This is rather like estimating the number of French-speakers in the US by citing figures which include Quebec.
What about those birth-rate differences? Native birth rates in western Europe, as in most developed regions, are quite low (the US is an exception), while the Muslim immgrants brought with them the demographic patterns of their Third World countries of origin. However, birth rates in most Third World countries have fallen to or below replacement level, or are in the process of doing so, just as those of the developed world did a few decades ago (continued population growth is due to the fact that such a high percentage of the current population is in the young-adult age bracket, which is the most fertile). One would expect this trend to be even stronger among European Muslims, surrounded by a prosperous and secular society, and indeed this turns out to be exactly the case -- Muslim and native birth rates in Europe are converging:
In Austria, for example, Muslim women had a total fertility rate (an estimate of lifetime births per woman) of 3.1 children per woman in 1981.....By 2001, the rate for Catholics had fallen to 1.3, but the Muslim rate had fallen to 2.3—leaving a difference of just one child per woman between Muslims and non-Muslims. The gap narrowed even further in the former West Germany.....In 1970, Turkish women living in West Germany had more than two more children than German women. By 1996, the difference between these two groups had fallen to one child. Recent trends in the Netherlands tell a similar story.....
I've noted the same trend in Denmark. A problem with collecting such data is a tendency to classify anyone born into a historically-Muslim ethnic group as being a Muslim; this ignores the growing phenomenon of de-Islamization. Many people counted as Muslims (because they are of Turkish or Pakistani or whatever descent) probably aren't.
Claims that western Europe is doomed to be demographically overwhelmed usually cite alarming numbers which in fact are obviously implausible (an example is analyzed here). One could argue that the United States is actually in greater danger of such a demographic take-over, since Christian fundamentalists here also have a significantly higher birth rate than the general population, and make up much more than 5% of all Americans (in reality, of course, all available data show religious belief declining in the US over the last few decades).
There is, of course, the issue of continuing immigration. But the EU has 450 million people and several individual countries have populations in the tens of millions; starting with such a large base population, no proposed or plausible level of immigration could produce the kind of radical demographic shifts that the alarmists predict. Mass public hostility to further immigration is high and rising, not only due to the cultural and political problems posed by Islam, but also due to sheer overcrowding (western Europe is far more densely populated than the US). Eventually the political system will have to respond; if leaders prove truly determined to ignore their voters' concerns -- well, I took a (rather pessimistic) look at the worst-case scenario here.
More generally, demographic projections over time-spans like fifty years are meaningless. Population trends are subject to all kinds of influences which cannot be anticipated. There is probably no major country whose present-day demographic profile could have been accurately predicted fifty years ago by extrapolating from trends which were visible then.
Western Europe is not going to become Islamized. Period.