A few things I'll write down that may or may not be meaningful/worth thinking about:

(i) I come from a culture with fairly repressed sexual norms. For most of my older male relatives, I'm pretty sure that up till the point they got married, their entire history of intimacy with the opposite sex comes from prostitution.

Most, when facing the much more open sexual culture in the West, will simply shy away. And yet likely a significant portion of young unmarried men will get the wrong idea, whether out of misunderstanding or pure maliciousness.

(ii) If you're a pure consequentialist, you might argue that giving a million people a chance at a better life are worth risking a few hundred people murdered, raped, or threatened every once a while. Nobody is a pure consequentialist. We're going to see that girl gang-raped in the streets as an victim, an victim of granting asylum. We're not going to see hypothetical hundreds of dead men or women in Syria as victims of not granting asylum. That is human nature, and serious progressives need to actually think about how to prevent victimization of natives before Europe descends into full-blown fascism (or perhaps it's already inevitable).

(iii) If native German women are reported being raped in the streets, imagine how bold the same criminals would be towards refugee women. Imagine how many cases of rapes of refugee women goes unreported. Cultural clash isn't merely a matter of communication. Cultural clash is social chaos, it's men with power (physical, or coercive) not understanding what is the right or wrong way to behave, and the victims are almost always the weak and powerless of each community - generally, women.

(iv) Assimilation has been successfully carried out for hundreds of years in the West, in places like Singapore and Madagascar and Brazil. Europe's current refugee policy has almost no discernable thought directed towards assimilation. In fact, it tries to celebrate diversity, because we see the second-generation Asian-American or fourth-generation Italian-American as "diverse". No, they're really just Americans.

What Europe is experiencing right now is true cultural diversity, and it sucks. But that is what modern liberal political thought has decided is "progressive", and the loudest fraction of people with such beliefs have been shouting down everything and everyone else as "fascism" for the last ten years. Good luck.