In 40 or so years if the Muslim population gains political control over most of western Europe will we see a mass migration of Europeans similar to early in the 20th century?
You mean in 40 years when European citizens of Muslim beliefs stand and win some elections in Europe? Why would people flee from their own fellow citizens?
Accepting the hypothetical, where would they go? The mass migrations in the late 19th/early 20th centuries were to the Americas. (Not just the U.S., places like Canada and Argentina got their fair share of immigrants too.) There are much more stringent immigration policies now.
I don’t see it as a likely outcome. Why would Europeans flee Europe because some Muslim citizens are elected to positions of power? 
Maybe they could move into the Middle East, which I’m assuming will be emptied out. All those Muslims must have left somewhere in order to go to Europe.
So you don’t see the muslim culture and religion working its way into the goverment? I have a lot of euro friends and as far as I know 100% of them are expressing dissatisfaction with the current assimilation of Muslims into western culture.
To be fair I also know a large group of local muslims who seem to be assimilating very well.
I think that the worry is that with a rapidly growing Islamic population we could see a government with a Islamic majority and the introduction of sharia law. The first signs will be local authorities with a Islamic majority and when this happens I think we will see the first signs of public unrest.
No, we won’t. Did you have any other questions?
But that’s really a matter of time. Look at the American experience with immigration since 1870 or so.
People come over, they bring their ways and language. There’s a huge protest against the - NO CATHOLICS NEED APPLY - and eventually their children and grandchildren assimilate into the larger culture. The culture adapts by making some havens and cultural touchstones adapted to the times.
100 years ago no one was getting drunk and wearing green plastic hats on St Patrick’s Day. Nor was eastern European Jewish culture so recognizable and acknowledged.
The Muslim immigration into Europe is in it’s ‘OMG they’re so DIFFERENT’ stage. These things take time.
Shrug, the “euro” I know closest is working with the Red Cross to offer her (currently unused) flat to be used as a waypoint location for refugees and other people needing a place for a few days to months. I’ve seen the Saharaui kid next door grow from a knee-high shy little bundle of black curls to a shy, taller-than-me teenaged boy.
I’m more worried about situations such as European countries which let lots of immigrants in but do not let them get jobs or schooling than about the fact that The Muslims Are Coming; we can’t put people in glass bowls and then complain they’re not integrating (well, we can, but it’s not going to be very helpful). Many of those coming (specially those from locations not at war) are coming because they do not like islamism any more than I do.
Are these friends about to explode, and therefore should be respected and listened to? 
Are you sure you want to go down that road…?
Here are the numbers. There are around 45,000,000 Muslims living in Europe. There are around 700,000,000 non-Muslims living in Europe. In order for the Muslims to have political control, they’d need to be a majority. So they’re going to need 650,000,000 more Muslims.
If you combine the entire populations of Algeria, Bahrain, Egypt, Iran, Iraq, Jordan, Kuwait, Lebanon, Libya, Morocco, Oman, Pakistan, Qatar, Saudi Arabia, Sudan, Syria, Tunisia, the United Arab Emirates, Western Sahara, and Yemen, it’s only around 595,000,000.
When my grandfather emigrated to the U.S. from Europe in 1908 did so hoping he’d get rich here, not because he was afraid of Muslims. I’m guessing there are still Europeans who feel that way.
People are pretty stubborn and aren’t especially given to picking up and moving thousands of miles unless they absolutely have to. Or unless the incentives to move are very great. Like free land, citizenship, and a chance to start over. If global climate changes were to make, say, Antarctica, a much more hospital place to live, then I could see mass migration happening. But I think it would come from all four corners, not just Europe. And it wouldn’t be driven by Muslims, but by economic opportunity.
Or more succinctly, the OP’s premise is flawed because the qualifying condition of “in 40 or so years if the Muslim population gains political control over most of western Europe” is utterly impossible.
If for some bizarre reason ( mass cloning with computerized in vitro Muslim indoctrination ) it were to approach reality, I’d expect a much nastier series of anti-Muslim pogroms. Because where exactly are 700 million non-Muslim Europeans going to go in just 40 years? Ascension Island?
But no, in real life people assimilate while subtly creating change and local cultures change into new local cultures. It’s how society works.
I’d expect that immigration controls will be imposed long before it gets close to that point. These are countries that mostly get their very names from the majority ethnic group. I don’t think many of those countries will allow the essential ethnic nature of their countries become compromised. Otherwise, you might as well change the names. They aren’t the United States, or Canada, or Australia. We’re talking about England, France, Germany, Poland, Italy, Spain. Those countries will always be English, French, German, Polish, Italian, and Spanish.
Tell that to the Catalans or the Basques ;). Or heck, the Alsatians and the Bretons.
European national homogeneity is over-stated and historically is less writ in stone than you might imagine. Southern Italy was once largely Greek-speaking and we’re not just talking pre-Roman era. There is a tiny Greek dialect-speaking remnant still.
The world changes, people change, languages change, cultures change. Trying to hold any of that in stasis is a fool’s errand.
You forgot the Scottish!
Europeans have lived under Islamic polities before - e.g. when the Ottomans controlled much of the Balkans. The period was not characterised by high emigration.
Periods of high emigration from Europe have all happened in Christian-dominated polities - from Tsarist Russa, from Imperial Germany, from Ireland when in the UK, from the Kingdom of Italy.
We might also note that, historically, the spread of Islam into new territories has not been characterised by mass migration of the population of those territories.
Had the OP paused to engage his brain before opening his mouth he would have noticed that European mass emigration has largely been driven by economic factors, not by religious-political struggles.
Sure, populations change. But it takes centuries.
Will Europe be majority Muslim a thousand years from now? Maybe. But I will confidently predict Europe will not be majority Muslim in forty years.