The Kajarites let that inclusiveness persist among the Yunani clergy in an attempt to pacify the non-Muslims and prevent the rise of the sort of fifth column that doomed Ummyadi Africa, at least according to al-Hasan. Of course, it backfired when said clergy supported Ismail Niqeforah in his rebellion over the foreign Kajarites...
Well, it's not like that didn't become a pattern for the Persian-Mesopotamian region: few dynasties could manage the juggle the complex politics of the religious mosaic of its thousand and one cults, despite the surprising ability of the region to keep coming out of its political turmoils more or less intact each time (albet under new management). Maybe if the Ummayads had stayed in Damascus or moved to, say, Egypt as opposed to relocating to Constantinople, they'd have been able to keep their geopolitical focus on Africa and the east long enough to prevent the overstrech that lead to the Crisis of 275 after the Revelation, keeping the Caliphate united long enough to mend their schism?
Sure, it might slow down the expansion of the Faith into Europe, giving Christianity time to stabilize itself and perhaps convert the Saxon-Norse Wodenites, Pict Erieian and Cymeric Druids, the Baltic Romuva, and other followers of the Native European religions to get some much needed support for the Bishop of Rome, as well as allow them to focus on blunting the Islamic invasions without the constant drain of resources in protecting the north. Is that worth the payoff of a more unified Faith in the heartland? Or do you think the conversion of even more populations to the God of Abraham would lead to a further discrediting of polytheism in general? Islam is, after all, pretty unique in its recognition of only one true God if we consider it compared to other globally notable religions, even if it is the largest out of all of them.