An interesting chart from the Economist about the perception and reality on the total number of Muslims in European countries. It's striking how big the overestimation gap is in the selected countries (do have in mind that these are the official figures; perhaps there are undocumented Muslim immigrants that increase the actual numbers, but I sincerely doubt that the real numbers are anywhere near the perception).
So why is there such a huge overestimation (between 3 to 8 times!) in Europe about the total number of Muslim population in their countries? In general, the anti-immigration sentiment rests on the same concept: that there are too many immigrants (many of which without any legal documents), "taking our jobs". The perception on the total number of minority immigrants in Western countries is very similar to this one from above. Their numbers are vastly overestimated.
Perhaps the reason for this is that minority immigrants tend to cluster in specific areas, primarily due to the cultural and language barrier of their new environment. Plus there is the perception held by the majority of Westerners that Islamic values are not compatible with the West. This makes the indigenous population hostile to newcomers, particularly if coming from Islamic countries (example: the current refugee crisis). As a consequence this turns entire neighborhoods of large cities into minority group ghettos, that tend to be correlated with higher incidences of crime and are considered unwelcoming and dangerous areas to live in.
The problem is actually cultural assimilation. Nothing is being done to assimilate the immigrants which are (in most cases) forced to start working in the grey economy, usually for their compatriots who came earlier. Greece has a particularly big problem in this department, as there is an entire underground market for undocumented workers. The immigrants get the low-paying jobs that aren't registered in the economy, and are getting paid over-the-counter. This is bad for both sides: the government doesn't get its tax revenues, while the workers are forced to work for scrap without any job benefits or security, all at the mercy of their local "landlords", or whatever we should call them. Naturally some of them will be encouraged to take up crime (or in the extreme case - terrorism). Failing to assimilate immigrants, in addition to causing social problems, is alienating an entire group of people virtually preventing them from ever adapting to the Western style of life. Perhaps it's not entirely their fault for not being able to assimilate. It's just that they've never been given an opportunity to do so. After all, the motivation for emigrating to the West is to enjoy a better lifestyle, to get the opportunity they never had the chance to take back home. They didn't come to work for nothing and to be treated like slaves. They didn't come to cause violence. The closed environment they ended up in pushes them in that direction. In the end this is hurting the economy in more ways than one. In addition to unpaid taxes, the labor force doesn't really benefit from undocumented workers.
So how should Western governments accommodate this? Scattering immigrants across the country or across different neighborhoods within a city, instead of letting them form clusters is one way of doing so. This is particularly applicable in the current European state of 'controlled' immigration (controlled in a sense that EU governments are documenting each immigrant and allocating them to a specific area). Another is to clamp down on tax evasion (and simplifying the tax code) which lowers the incentives to work in the grey economy, and as a consequence resort to crime and violence. None of these may be enough to assimilate new immigrants completely, however complete assimilation never does actually happen to first-generation immigrants. It's the second generation and beyond (the ones that are raised in the new environment) that become fully integrated into new culture. The reason why this isn't happening in many European countries isn't the impossibility of Muslim cultural assimilation, it's the specific clustering they amass to which never really presents any opportunity for the newcomers, making them think that being in the West is not that special after all. This fuels anger. On both sides actually. And hence the overestimated perception.