Muslim states dominated the subcontinent from what, ~1200 to ~1750? Over the same length of time of about 600 years from conquest Egypt had only very recently lost its Christian majority and there were still large religious minorities in the Levant and Iran.
This is a very relevant point! The Islamization of much of the Eastern Mediterranean was an extremely gradual process, and much of the region only became overwhelmingly Muslim in the very recent (aka 20th Century) past.
And of course there are still very large non-Muslim minorities in that part of the Middle East--even excluding the recent immigration of Jews to Israel, there are still lots of Coptic Christians in Egypt, Arab Christians in the Levant, Druze, arguably Alawites, etc. And you don't have to go far to find many minorities in Kurdistan, though many were targeted by ISIS.
Really you also have comparable religious diversity in most of the Muslim world outside of Arabia and the Maghreb*, and in places where you don't it's usually a function of very recent persecution or mass migration (Iran, Pakistan, Turkey, etc.)
*As an aside, why did Christianity hang on for much less long in the Maghreb?
I remember reading that the Holy Land that the Crusaders came to was majority Christian. I'd have to research the topic to say for sure, but it sounds quite possible that the Crusades helped pave the way for Christianity to become in the minority in the broader region, simply by their death toll.
In regards to Turkey, it's important to note that it provides among the best examples of the mass migration and persecution that you speak of. Many Circassians (and other groups impacted by Russia's move south) were resettled in Anatolia by the Ottoman Empire, and the Armenian Genocide and the population exchanges between Turkey and Greece must have had an impact on the religious demographics of the region more broadly, though precisely how much I'm not sure.
