There's also the chance that they might predominantly identify as Arab, since this identity is so inclusive (only language requirement).
As for how they would look like, it depends on the location. France's Muslims are quite different from Sweden's ones.
This is what happened to White settlers of America. They were predominantly of Christian backgrounds, but ethnically diverse when they first got here (English, Irish, German, Danish, Norwegian, Swede, later Italians were accepted as being White when first they were not).
They were even concentrated in specific neighborhoods/cities just like more recent ethnic migrants are (all throughout the US, there are formerly Little Bulgaria, Little Germany, Little *insert country of European origin here*, etc...I think Little Italy is the only one standing today in any significant way), but they eventually lost their specific ethnic identities (language and ethnic culture) and blended with other White settlers to produce the Christian American mutt, who is simply “White”.
For this reason, I can buy the “Muslim ethnic class” hypothetical.
As time goes on and they identify as American Muslims and can no longer connect with the ethnic culture of their forbears who first immigrated here, it’s entirely possible they’ll mix with other American Muslims to become Muslim mutts, and religion will be the only identifier. As more time goes on, many of them would likely lose the religion as well just as a good portion of American Whites are fairly irreligious now in terms of Christianity.
But the idea that they would identify as Arab is farfetched, bc they wouldn’t be speaking Arabic nor would they be in contact with Arabs. At best, the vast majority would be English speakers who utter Arab ayat from the Islamic literature without understanding, and only a select few would learn the Arab language for scholarly purposes (Islamic theology). It’s far more likely that the term “Muslim” will morph into a pseudoethnic term as well as being a religious term (just like the term Jew).
