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Europeans have not been having enough babies to keep their populations stable for the last 30 - 40 years. Ergo, their populations are now shrinking radically and aging radically. Ergo, they must have guest workers.
It would take a tremendous act of political will for them to shut the immigration door under these circumstances. When you add to that the fact that the dominant political power in Europe, the soft tyranny of the socially tolerant state, decries any resistance to the Muslim threat as racism; you have a sure fire formula for suicide.

[Question_Assumptions]

It is an interesting problem that the freedom that Western civilization grants women is excercised, in part, by having few or no children, which, in turn, endangers those very freedoms by creating a demographic shift to those cultures who do not let women opt out of childbearing.