Not that I'm aware of, and certainly not down to today. I say that last part because accurate censuses including religious data are virtually unheard of in the Middle East since the end of the colonial era.

If you look at the sourcing for the most frequently cited such modern maps, from Dr. Michael Izady's collection here, you'll find that very often the source of his data is from the the 1930s or earlier.

His religious map of Iraq is typical: http://gulf2000.columbia.edu/images/maps/Iraq_Religions_detailed_lg.png

If you look at the very small fine print on his sources in the bottom left corner you'll find that almost all of his most relevant sources are from colonial demographic studies in the 1910s or even the 19th century.

I see these maps so frequently as purporting to represent present populations that I have to wonder at whether his failure to make the dated-ness of his sourcing clearer isn't deliberately misleading.

In any event, the precise religious demography for the much of the Middle East in most Middle Eastern countries from independence to the present is basically educated guesswork, estimation, and rough polling.