Zoroastrian was the state religion of the Sassanian Empire. Despite this, it was not the majority religion, there were significant Christian, Jewish, and even Buddhist (if memory serves me correct) populations. Zoroastrianism was reserved for the ruling elite, the aristocracy. Likewise, when it was conquered by Arab forces, it was subject to attack. Holy sites like fire temples were desecrated and destroyed, they may have even been converted to Islamic places of worship. The jizya, a tax for non-Muslims, also would have played a role for influencing conversion over time. Zoroastrian is still practiced today, the largest communities being in Iran and India.

Sorry for the lack of a source, currently I am abroad and for the life of me can't remember the name of the author I'm drawing from.