The way this manifests is different in each country, but the fundamental reason is the same. In the german case, take the words of Messut Ozil, the former footballer - when the German team wins, he is German. Lose, and he is the immigrant. He is ethnically Turkish, i.e. not ethnically German.
The same will apply to your kids as well.
I want to be clear, not every German person is a frothing racist, i would argue that the racists are a minority. It is, however, important to note that the reactions of the individual and the reactions of society can be different, sometimes polar opposites.
In sharp contrast to this are the US and Canada, where there is no shared definition of "white" even though the majority of their populations are ethnically European. In that case, "European" spans everything from Irish and Greek, to French and Austrian. Less than a hundred years back, Irish people were not seen as white. Today, that idea is laughable. The fundamental difference between the US and Canada on one side and German or european society on the other is that the old world is built around exclusion, while the new world is built around inclusion.
This is one important reason why skilled immigrants leave europe, and is also why i left.