Was that true at the time? They were certainly ruled by a caliphate, but other religions survive in Persia till this day so I wouldn't be surprised if the process took centuries. There also appears to be some repression of Persian people after. That Viking could of also been a refugee of the islamification process or the various power struggles in the region at the time.
Just to be clear, what is known as Persia is a subset of modern day Iran:
http://www.heritageinstitute.com/zoroastrianism/iranpersia
Quick note about non-Islamic religions in Iran:
https://en.m.wikipedia.org/wiki/Religion_in_Iran
"The remaining 0.6% associate themselves with non-Islamic religious minorities, including Bahá'ís, Mandeans, Yarsanis, Zoroastrians, Jews, and Christians. The latter three minority religions are officially recognized and protected, and have reserved seats in the Iran parliament."