The US has had waves upon waves of immigrants of various nationalities, and we still have a similar "identity" to that we had before. I know it's a bit different for one of the long-established countries in Europe, but you have to assume not only will the immigrant population outnumber the native population, but that it will actively seek to overtake the culture and that the dominant controlling forces of the culture (pop cultures stars, chefs, politicians, etc...) will also become dominated by the immigrant group.

I'm not saying that these things will or won't happen, but I would personally rather side on the err of letting people be themselves. In fact, I rather believe everything would go a lot more smoothly if everyone just took a big deep breath and moved on with life.