No, there's no Muslim invasion of Europe or Germany, and we don't turn Muslim anytime soon either. I mean this century (and I very much doubt religion will have much of a niche left in the 22nd century).
What's happening in Germany right now is not a defence issue, nor a disaster or whatever. It's a domestic cultural conflict; a domestic political battle with xenophobia. Xenophobes and other fringe people have made 'progress' first out of sight by organising and preparing BS propaganda and BS theories, and since last year also by daring to enter the sunlight. Suddenly (by joining conspiracy theorists and protest groups with more or less valid points) xenophobia was fit enough for respectable political rally sizes and quantities (in a handful of cities). They even infiltrated and overwhelmed a small fresh party of disillusioned conservatives who disliked the mainstream CDU/CSU parties.
Federal-level politicians sat this out and didn't do much about it, but the brazenness increased and xenophobes produced quite a string of arson incidents on uninhabited buildings meant to house immigrants in the future.
This was when national media, national-level politicians up to the Chancellor etc. decided to lead a political counteroffensive, choosing the immigrant / "refugee" issue to take a stand.
I think they choose the site of their battle poorly, and there may be a horrible backlash to their policy (because these "refugees" actually ceased being legitimate civil war refugees when they decided to leave safe havens in Turkey and Jordan and began passing through several safe haven countries to seek out the more wealthy destination Germany). A Pyrrhic victory is likely.
Even with several billion Euro spending per year for this mess (half of it flows back as taxes anyway), the bigger issue is the ongoing battle between the mainstream and the xenophobic fringe.
Even a million immigrants wouldn't make much of a dent in German demographics, and in the long term their fertility will approach the typical German fertility rate anyway. The vast majority of our past "Muslim" immigrants are now secular and disinterested in religion, whereas but a few thousand of them (and converts) ever turned into Salafists and the like - the "Muslim" contribution to the fringe in this country.