The country has at least four major religions and four official languages with considerably larger minorities than any European country, yet, has not seen a race-based breakdown in the rule of law in decades.
It's a failure of government when the rule of law breaks down. It's up to the citizen to figure out the problems and solve them with their votes and by talking to their elected politicians. What have you personally done politically to change the situation in your own country? Personally, I've given up and emigrated to a country with better individual rights.
I'm not sure closing all borders and living in autarky (which is where the UK and US seem to be heading) is a good long term choice. Not my countries, not my problem. It saddens me a little nevertheless to see so many great countries pick it.
Singapore even outright discusses how fast infrastructure and services are growing and sets the amount of immigration for the year accordingly. I suspect if Germany really was willing to take up the majority of the million Syrian refugees (and mass immigration from any other country in distress), it would make sure to invest accordingly and be able to integrate that many as the US has done in the early 20th century [1] (so much for history). If they get it right, it might be a huge economic boom and great long term move.
As for "the common German belief/societal structures", no culture is stagnant (and clearly not German values, if you look at the 20th century alone!). Even the US is a strange mix of a dozen traditions, cultures and habits which have blended into "American".
For example, most world citizen think of the US, not Italy, when eating a slice of pizza. People call a flat white Australian, but the Australian coffee culture which is spreading globally today is a direct descendant of Italian immigration to the country. Immigrants adapt to the local custom (cf "Chinese-American" food, secularisation of the second generation, etc.) and the country adapts to its immigrants.
[1] "between 1880 and 1920 [...] brought more than 4 million Italians to America" (https://en.wikipedia.org/wiki/Italian_American) - this when the total US population in 1920 was 104 million (https://en.wikipedia.org/wiki/1920_United_States_Census). How many famous Americans today, like Rudy Giuliani, Jay Leno or Madonna have Italian origins?