Loveunihateexams,
I think that is an interesting question. Lots of Muslims have successfully integrated in the US, and as in most immigrant groups, there are some older language holdouts, but most are successfully starting busing, crazy to get their kids high degrees and work their butts off to do it. I know businessmen, doctors, engineers, entrepreneurs, teachers, etc.
In Muslim countries, English is defector business language, which is convenient for most westerners, but when westerners are expected to follow cultural norms (to a lesser degree) and are punished according to their laws, the world has a collective panic attack. Yet we all get in a huff if ladies don't cast off all modesty upon arrival. I worked and lived in several predominantly Muslim nations. Not even in Saudi is a western or non Muslim woman expected to cover her hair, although she is supposed to cover her limbs. In Pakistan, many don't cover. In Egypt, there is a total range of degrees of covering. In Qatar, also. No one told me to go back home. Ever. My language issues were accommodated as well as possible(usually impressively) I did go to Makkah. I did not wear an abaya or black. I was modest, but I'm not Arabic, and my cultural version of modesty didn't look like theirs, except for one day after I bought an abaya. It still was not black, but fyi, lots of abayas are not.
Many Muslim women in the US are modest but if they did not cover their hair, you'd think nothing of it. Some still wear abayas. Many are indistinguishable. We are much better integrated than many will acknowledge. That's a shame.
There is a learning curve for any immigrant or visiting group. Hello, Americans going to Europe have some real adjustments to make. Especially older ones who are more set in their ways. My mom is a real "ugly American" even out of her neighborhood. I shudder to think what she did in Italy, Greece and Turkey.
Your doctor, lawyer or insurance agent or IT manager at work may be able to tell you about integrating and the challenges they faced.