You can't perfectly preserve your culture when you let in immigrants on the scale that, say, Germany is. It's sort of a sliding scale; the more you let in, the more you change. Europe will be changed for this.
As you should be able to tell from my earlier comment, I do empathize with the migrants. It's a shitty situation, and were I in one of these war-torn country, my top priority would be getting my family out of there. But the laws and immigration policies of Western countries are crafted by the current citizens and should be moulded to their benefit, not a universal altruistic ideal. By my interpretation, that would be limiting immigration to a number that can be reasonably integrated to the host culture. Immigration to Europe currently far exceeds this.
I'm sorry if my mentioning rape offends, but I don't think we can have an encompassing discussion of migrants without at least mentioning it. I could have also mentioned migrants' attitudes towards women, LBGTs, freedom of speech, or freedom of religion. These are not views I want any sizable number of people in my democracy holding.
I'll be happy to pay more tax if it helps solve the problem.
However I see Merkels let-them-come attitude as dangerous feel-good politics.
Why?
1. Because moving that many people around creates dangerous (for us and them) conflicts.
2. Because for every refugee we help in Europe we let down 100 in the middle east. Why? Because it costs enourmously much more to help people here than to help them down there.
So - IMO - today's feel-good let-them-come policy should be replaced with a targeted approach aimed at helping them where they are or in neighbouring countries.
As I said I'll be happy to pay more a little more tax for this.
Bringing up incidents of rape in the abstract like that is unwarranted and inappropriate in the context of the point you're trying to make.
Think about how you'd feel if you were in the situation of migrants/refugees.