Its a little more complicated than that, Constantine was not compelled to become a Christian. Christians remained a minority inside of the Empire until well after Constantine won the empire and converted. The institution of emperor actually was the main catalyst for the transformation in the first place. Persia's Zoroastrians were never the dominant faith among the people, only among the ruling classes. Manichean and Christian, and even some Buddhist missionaries had converted most of the populous at the point of the invasion by Khosrau II. Given litergical differences between the Christians in Persia and the Christians in Rome, cooperation between the two did not appear to happen often. Zorastrianism at this time was also quite different from Achaemenid Persia, which resulted in its largely being absorbed into the Abrahamic understanding of the world. While distinctly different, Judaic, Christian, and Manichean influences had more or less transformed the faith into a monotheism, and the royal family had a handful of Jewish marriages, even from the very beginning. This meant that Persia was never really considered Pagan, just not Christian. Muhammad and the Caliphate would eventually claim that the Zoroastrians were people of the book, and placed on a like level with Christians and Jews. This was not purely motivated by political realities, but by common cultural understanding. As a result Zoroastrianism was not seen with as much hatred as Pagan cults would otherwise receive in Rome as demographics flipped in their favor. Furthermore, Zoroastrianism was a fundamental marker of the Persian monarchical and administrative identity. Them converting on their own would be a very tricky proposition, and would most likely only occur during a period of civil war where an appeal was made to gather popular support.