This thread covers a lot of aspects of Islam taking hold in Iran. One thing not mentioned in the thread (and also a bit off topic for this one) was that Persians had a (arguably) much stronger reaction against the spread of the Arabic language than the spread of Islam. When Al-Hajjaj ibn Yusuf arrived in Iran, he tried to discourage, and eventually ban Persian and made Arabic the official language. This (along with the invasion of Islam in Persia) sparked lots of civil unrest to the point where Caliph Umar was assassinated by Piruz Nahavandi and many of the provinces in North and East Persia fostered insurgencies. I think it can be argued that the Persians keeping their language saved their empire and culture from being subjugated and eventually absorbed by the Arabs. Similarly, the Levantine people who spoke Hebrew, Phoenician and Erkonite were absorbed by the Arab invaders and the latter two are currently extinced, the former surviving with the Jewish people. In Lebanon, Syria and Palestine they speak Arabic and follow Arab customs. Also linked in that thread was Drinking Arak Off an Ayatollah's Beard by Nicholas Jubber which is a great unbiased book on the Iranian peoples acceptance and views of Islam in modern and medieval Iran.
A similar question was asked to which I gave an extensive answer, hopefully it can help https://www.reddit.com/r/AskHistorians/comments/3iiek8/how_did_islam_take_root_so_well_in_the_persian/