Well there is not much evidence so far, that Muslim immigrants to America are particularly lawless. In fact, they tend so far to be middle to upper middle class. But then, the numbers have been rather small. The most elite immigrants are Indians from India. They have the highest per capita income, of any ethnic group in America, beating out Jews and Greeks, who are the runner ups.
There is some truth in your observation regarding Middle-Eastern immigrants. And the observation may hold true in perpetuity. On the other hand, niether of us knows what events might take place that would cause a shift to a different reality.
The seeds were planted since childhood. Given a little rain, who knows. Sadly, none of us.
There are many people in the world who live in nations where the U.S. is respected. I have never understood the impetus to immigrate people from terrorist states vs them.