I moved from the US to Germany and lived there for almost 7 years. Even as someone with German ancestry (from 5 generations ago), a German last name, and enough language skills to get by, you never really fit in. Germans are insular in a way that, I suppose, all people are, but a special kind of matter-of-fact curtness that is off-putting. Younger Germans are embarrassed by it and make a show of welcoming outsiders (…
It also depends on your social circles and where in Germany you are. If you are in Berlin or Hamburg being German won't matter too much. If you are in the suburbs of shouthern or eastern German cities, much more so. If you are in the creative world of Berlin you might get away without talking German at all.
Given it's comparedly small size Germany has a surprisingly diverse regional culture, which is why people who know the regions well usually lough at the idea of something that is "real German". Or as the Austrians say it: "What divides us from the Germans, is the common language" and I'd argue Bavarian and northern German culture is equally far apart.