They aren't trying to "take over the world". But many of them do wish to practice their religion the way they do in their home countries, including the enforcement of Islamic laws and penal codes; and they are a rapidly growing minority in just about every country that accepts immigration. With current immigration rates continuing, this population is projected to eventually become the majority in multiple European countries, or at the very least a significant minority. That is where the "take over" part comes from. Not through uprising, conspiracy, some calamitous agenda, or any intentional or planned manner, but through basic statistics and the nature of democracy.
Here is skimming the surface of the difference, and the crux of the issue:
How many cultures are there left in the world that still practice fundamental Judaism? I use Judaism because the extreme judicial sections of the Christian Bible are from the Old Testament, which was Judaism, the New Testament being the source literature of Christianity doesn't contain laws, rather it teaches to how to live as Christians under any number of legal systems as examples and forces of influence to those around and over them (give unto Caesar, pray for your leaders, light unto the world).
What country in the world still stones adolescence for disrespecting their parents, under the rules of Judaism? What country in the world still stones adulterous women, or forces their citizens to follow the strict Levitical laws of atonement for various crimes or even for normal biological occurrences (menses)?
The answer is none. Not even Israel practices these things, and they sure don't force their citizens to do them. Many of the things required in the Old Testament would even be illegal for a citizen to do in Israel.
However, you have numerous countries that practice and enforce the strict, violent, and misogynistic laws of Islam.
So naturally it is going to be a problem when immigration has pools of people from these places moving to modern and mostly secular countries who carry with them a desire to practice and uphold their religious laws. This is why we constantly hear talk about Sharia Law. We have continuous and rapidly growing communities of immigrants from these countries who feel it ought to be their religious right to practice Sharia law in their host countries.
It would be great to provide that kind of religious freedom to Muslim immigrants, unfortunately this form of law also brings along a lot of human rights violations. It wasn't that long ago I posted several stories on the prevalence of gang rapes in communities of immigrants from some of these countries in places like Sweden and France. It is out of control and the local police have a hard time policing it, because so many in those communities are behind it and keep it secret. Their attitudes are that it is their communities business, not the business of the secular French (or whatever country) government. It is the way they do things back home, the way their religion and culture teaches, and the proper way to do it.
Anyone can see how this can become a real legit issue. It is great to be all multicultural, and to welcome immigration, be non judgmental, and have a laissez faire stance toward other religions and their practices. But a line has to be drawn. When it becomes a choice between being politically correct and pro-freedom of religion and human rights violations, then political correctness and freedom of religion are the things that need to take the dive.