Os 8 parlamentares muçulmanos na Alemanha votaram a favor do casamento gay

Aqui (página em alemão traduzida). Isso só mostra a força de uma sociedade aberta e moderna. Os imigrantes acabam adotando, ao menos na esfera pública,  os valores da sociedade secular.
Outra evidência:

The majority of Muslims in Germany are devout and open-minded at the same time. The study shows that 63 percent of those adherents of Islam who consider themselves fairly or very religious say they re-examine their religious attitudes at regular intervals. Roughly 60 percent of those respondents say they support same-sex marriage, something that also applies to 40 percent of highly religious Muslims who say they rarely look at their religious principles. In Turkey, in contrast, the country of origin for most of Germany’s Muslims, only one-third of highly religious Muslims say they regularly re-examine their religious beliefs. Only 12 percent of highly religious Muslims in Turkey say they are in favor of same-sex marriage.

Outro paper corrobora a ideia: "Does mass immigration destroy institutions? 1990s Israel as a natural experiment" (versão aberta aqui). Os autores mostram que a chegada de russos não teve qualquer efeito ruim sobre as instituições locais.