It's funny that you say that about ignorance of foreign cultures. I immigrated to Germany myself, and am in the US currently for uni/career.

Americans are definitely ignorant about a lot of stuff regarding Europe, and those 3rd generation Americans often do piss me off, but Germans are incredibly ignorant about East Asia, something that Americans, at least in California, are infinitely better in.

Europeans know Europe better than non-Europeans do. That's not bad, considering that East Asians tend to know nothing outside of their own country and Japan or China. Still, from my experience, Californians are the only group of people to consistently try and look past their own continent.

Relatively ignorant about Europe? Yes, but much better than if you ask a Taiwanese person about a European country. Hong Kong/UK, Japan/Germany, rich people/London+Paris aside, no one really knows anything at all.

Relatively ignorant about Asia? Yes, but at the same time much better than most Europeans. People know better than to call us a province of China, or confuse Japan with Korea (really don't understand this one, it's like confusing Cold War America with the Soviet Union.)

I don't know, that just seems like a bad stereotype to me. Even after living here for a couple years, I'm still ignorant of the culture of most of North America. Rather simplified, but the cultures of North America is pretty much just separated into Chinese people, Korean people, rich Americans, rednecks, nice Canadians, and mean Canadians to me. Given how different everything is here from place to place, wouldn't that be the same as being ignorant of various countries in Europe?