Zoroastrianism was already on its way out, so Christianity was already extremely popular.
My POD could be an organized resistance to the Arabs as they were invading the Iranian highlands. The Arab general who led the offensive against the Persians dies from an arrow could be a possibility? Maybe the houses of the collapsed empire band together and fight the Arabs out. A new Shahanshah rises from the ashes and is a Nestorian christian..
Except Christianity was only popular amongst non Iranian subjects, mainly Semitic Aramaens and Arabs, rather than the ruling class which was firmly Zoroastrian. Christianity and Manichaeism were seen as lesser religions rather the religion of a dignified Aryan. Zoroastrianism is not going to be beaten in Iran without a conquest.
But the Arab general situation is interesting nonetheless, not saying it isn't possible having a Christian Iran, just needs to be more inventive than just saying Zoroastrianism was on the way out.