In the US, impoverished immigrants in need of social services and likely to be illegal are almost exclusively Hispanic. Immigrants who can afford transoceanic travel tend to be more-or-less middle-class, or at least have personal connections to established US citizens.

I realize that in European countries, much closer to the Middle East, the cheap-immigrant-labor pool includes plenty of Muslims, but this is not so in the Western Hemisphere. Our illegal Muslim immigrants generally arrive legally (typically with student visas), and become illegal only after overstaying their time.