If you live anywhere in the Southwest, it would be very easy for someone of middle Eastern descent to blend in.
Do they also take intensive conversational Spanish in order to do this?
Not all Hispanics speak Spanish -- they can just use the excuse they were born and raised in the USA.
What?!? There's no way that any person born and raised in the Southwest would ever in a million years mistake a ME for a Mexican. There's the obvious physical differences - skin color and condition, hair texture, eyes, facial structure, hand to palm color and texture, etc. FYI, just because they both have brown skin does not make it the same hues or texture. Not to mention the fact that Mexicans don't speak Spanish but Mexican with their own Americanized phrasing. That ME accent, no matter how hard they tried to hide it, would be a dead giveaway.