It seems to me that I've read that several spirits or avatars are flipped in their moral significance between Zoroastrianism and its relatives on the one hand, and Hinduism on the other. Compare the Western concept of devils (evil) to the Hindu Devas (good). As I remember the argument, Zoroastrian and Hindu civilizations therefore have the potential to misunderstand each other as "Satan-worshipers." So Zoroastrian survival in Iran may may not be the best way to bind the civilizations together. This is also a major obstacle to mass conversions from one of these faiths to the other.
I do think an Iran that stays Sunni, and a North India that stays Sunni-ruled, will be considered even closer relatives than the two zones are OTL. I don't think mass conversions are necessarily required for this perception to arise. And it's not completely impossible for a massive Timurid-style empire to retain control of both. Unlikely in the long term, but one could last long enough to further bolster the perception of a common cultural zone.
Beyond that, maybe a Seleucid Empire that retains the Iranian Plateau for longer imports Buddhism from Bactria, and Buddhism wins out in at least parts of the subcontinent as well. Depending on the later history of Southeast Asia, we may see ATL social scientists categorize the "Indosphere" as a zone stretching from the Zagros to the Mekong.
Christianity made some inroads in both civilizations as well, but seeing either, much less both, assume a Christian identity is far more unlikely than any of these other possibilities.