So problem, it seems like is not the multiple cultures residing in Germany but German immigration policies.
If it seems that way to you, then you're simply wrong in your analysis and conclusion. Everywhere in the world the problem is between two cultures. The English-French divide in Canada didn't arise via immigration, it's a problem between two cultures. The same cultural issue between the Czechs and the Slovaks. The same between the Hutu and the Tutsi. Coming back to the Canada example - Canada had a massive influx of Poles, Ukrainians, Scots, Irish, Dutch, Germans and when they settled across English Canada, assumed a Canadian identity, all of the immigration related issues faded away. What remains is the divide between Quebecois culture and English culture (people with descendent of Poles, Slovaks, Dutch, etc).
Germany should learn to distinguish between normal people and terrorists. They are not on and the same. This shows that the issue of Islamic fundamentalists making into Germany has nothing to do with multiple cultures.
No, the root problem is with Muslim immigrants. German has immigrants from Japan and Vietnam and other Asian countries and they seem to get along well enough.
If Muslim immigrants to Germany converted to Catholicism or Protestantism, changed their names to German names, avoid associations with other Muslim communities and instead integrated deeply in a German social network, then they'd eventually become Germans with a darker complexion. But they don't want to be Germans, they want to be Muslims, they keep their languages and customs alive, they keep their distinctive names - they're economic migrants who really don't have an appreciation for German culture, they just want the enhanced lifestyle that comes from living in Germany.
To be a Muslim means that you believe in the foundational beliefs of Islam and the foundational beliefs of Islam ARE THE PROBLEM.
It seems like some racist elements inside Germany want to limit immigration of people of color under the pretext of failed integration of multiple cultures.
There's absolutely nothing racist about wanting to maintain one's community. No one has to offer excuses for saying "Germany for Germans only, Germany for whites only."