I'm unable to answer your question but I'd like to point out that there is a problematic assumption in it, viz. that Christians "felt they couldn't co-exist with polytheists and tried to wipe them out".

Christians co-existed in a generally peaceful fashion (well, the violence tended to go one way, that is, pagans to Christians) with polytheists in the Roman Empire for at least the first four centuries of its existence. Salvian, a Christian bishop in a Christian-majority empire writing ca. 440, is quite tolerant towards pagans both morally and socially, and earlier, looking to e.g. Augustine, we see in his parents a Christian woman marrying a pagan man. When the Christian world expanded and made contact with other pagan peoples there were, indeed, attempts at "wiping them out" (e.g. the conquest of the New World under the Castilian empire-- but this is a bit more complex as they saw the New World as rightfully their own territory and thus the natives were understood as citizens of a Christian empire) but there are plenty of examples where this wasn't the case (e.g. Christians in Japan from the 16th century onwards).

I'm not expert on Zoroastrian rule, but as far as I know, the Persians generally allowed local religious territories in the areas they controlled. While there was adoption of Zoroastrianism by some, unlike the Christian and Muslim Empires, there was no long term incentive to make the world Zoroastrian, to my mind, there was no presumption that this was the ultimate goal. Zoroastrianism was tied much more to a specific "peoplehood" than it was a universal religion (I'm sure this changed at various times, but just in general). Before the period you're asking about, but in the Achamenid period, Cyrus famously ordered the rebuilding of the Temple in Jerusalem, but that's not all he ordered rebuilt. The Cyrus Cylinder orders the rebuilding of many other (non-monotheistic) temples as well. Whether this sort of thing continued in the Parthian and Sasanian Empires, I don't know (in both of those, the population was generally more homogenous with a clearer core around the already mostly Zoroastrian Iranian Plateau so the issue just came up less).

That said, I'll also point out that during Christianity's slow spread throughout Europe (and then the world), there were both moments of co-existence and moments of rapid and conversion. We mark clear dates on a calendar for "conversion" to Christianity in non-Roman Europe, but those are generally moments where the leader converted. Non-monoethistic practices often lingered on in places much, much longer. Islam is similar, but if anything the toleration is even more obvious, more explicitly tied to state policy--look at Mughal India, for example, or early Islamic Indonesia. There we see Muslim Empires with large non-Muslim, non-"peoples of the book" populations. While the conversion of Arabia from Polytheism was seemingly immediate and without coexistence, that wasn't actually generally the pattern you see in Africa or Asia where the conversion was much slower and there were long periods of Muslims and non-Muslims living side by side--usually with the non-Muslims slowly, not rapidly, converting. You're still seeing (some) conversion to Islam from polytheism in places like Indonesia and Sudan, though the coming of Christianity as a rival for Islam has changed the process quite a bit, with many opting to convert to Christianity instead in order to maintain their difference from the ruling group.