It seems like American Muslims tend to be more socially/religiously liberal compared to European Muslims, why is this?
A higher ratio of muslims increases the chance to form a parallel society in which you are actually able to live in the country without really speaking the language of said country. You tend to "stay together" which contradicts the multicultural approach.
But to be perfectly clear: This goes both ways.
My father immigrated in the 70s from Turkey to Germany, being a construction worker for all those years he never really learned the german language, which is his failing, but from the beginning they were viewed as "Guests" who would work here for decades to just leave when they were not needed anymore.
And in most cases these people were just not educated...like at all. The only reason they immigrated is because of economical anxieties in their home countries, no work, no future etc.
So you have a lot of uneducated, muslim people, who are just not adapted to this lifestyle, so they are forming their own world, kind of separated to the native world.
Now times are indeed changing, but there is also the second generation which, in some cases, just couldn't adapt also, because they are basically living two lives.
My whole life I only spoke turkish at home and when I'm out for school and friends I generally speak german of course and to be quite honest: This is not for everyone.
Living two lives influences their school, their behavior, nearly everything. Failing in school you can't really expect much help from your parents, because...well, you know why.
As consequence you will reach a point where you feel useless and helpless and this is exactly the point where the extremists want to see you, because only then you will be able to accept their fiendish thinking.
It all boils down to uneducated people, who just doesn't feel accepted in society. These are my observations.