What is important is that the rule of law and individual rights do not break down or become unequally applied. If justice and the police scale with the influx, refugees can integrate well and fast, even if their food and home practices might look different. If you let ghettos develop, you have a problem. In your example, the solution is not to let women or gays be oppressed, and not allow sharia courts to supercede the governmental ones. People can retain their views so long as they don't actually go on and infringe on the rights of others, if they do they go to jail.

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?