Wouldn’t most Middle Eastern Muslims qualify as Caucasian, i.e., “white”?
No because even most “WHITE people” don’t qualify as “caucasian” (which is not the term used by much of the rest of the world).
Most Iranians, and most of the Muslims in the southern Former USSR and in the Slavic nations and even Northern Afghanistan are as Lily White as Andrea Mitchell.
I'm sure all those lily white Muslims are terribly offended that she has not converted fully to Islam. She is, after all, one of Islam's most prominent defenders. She owes it to Allah to make the full conversion.