I mean, the Persian Empire was pretty big and most Persians were of that faith. In the Ottoman or other Islamic empires you don't see such a large scale conversion, and Arab Christians remained after the expansion of Islam of the 4 caliphs.
Just to preface: Zoroastrianism in Iran was not very centralized. Remember that the territories of the various Iranian empires were vast AND very sparsely populated, a characteristic that hasn't changed even today. Zoroastrianism in many territories wasn't an organized religion but an amalgamation of both religious and cultural rites, if that makes sense. The Zoroastrianism practiced in the Central Asian Steppes would be much different than the Zoroastrianism practiced around the Persian Gulf, for example. There was no real central authority and even the Avestan texts were not "set in stone" as the central authority. Aside from Zoroastrian clergy in major cities, there was no single clerical body to resist conversion.
Now, it is also important to note that conversion to Islam was not immediate and took nearly 500 years before Iran became majority Muslim. So what facilitated this conversion?
The Umayyad Caliphate was exclusive to Arab nobility. They even went so far as to discourage conversion as it would mean allowing more non-Arabs into the "club" so to speak. It also was the catalyst for the Iranian-led Abbasid Revolts, which resulted in the far more cosmopolitan Abbasid Caliphate. Both of the Caliphates, but more principally the Abbasid Caliphate, were based heavily on the Sassanid system of bureaucracy. Many famous viziers, and government officals were Iranians. The Arabs were well aware that the Persians had been in charge of Empires for 1000+ years and employed them dutifully to run the new caliphates. However, in order to be employed by the Caliphate, one must be a Muslim. So many Iranians would simply convert for this reason. Many former Zoroastrian clergy and their families would completely convert to Islam, most famously the founders of Samanid dynasty.
Zoroastrians were quickly granted dhimmi status, meaning they are respected as people of the book but would have more legal limitations compared to Muslims such as having to pay additional tax. Money talks, and this was another way that many Iranians converted to Islam
Many of the practices and concepts in Islam were already very familiar to Zoroastrians. Zoroastrianism was (unless you want to get technical) monotheistic, had the same concept of heaven and hell (still used in Persian today: pardiz [cognate paradise] and doozakh for "heaven and hell"; compare w/ Arabic jannat and jahanam), the same apocalyptic end-of-days battle between good an evil, a force of good vs. a force of evil (god vs. satan), multiple prayer times throughout the day... the list is pretty extensive. It wouldn't be very difficult for a Zoroastrian to switch to Islam in terms of religious practice and belief in return for more lax legal restrictions.
Many Iranians saw the Zoroastrian clergy--almost all nobility--as having too much of a stranglehold over society in a very typical Indo-Iranian Caste system. Converting to Islam would, theoretically, break you free of the chains of class--similar to the logic used by many Muslim converts in Hindustan.
As more and more Iranians became Muslims, the center of the Eastern Muslim world eventually focused around Iran itself. Baghdad, the capital of the Abbasid Caliphate, is a Persian name meaning "god-given". Iranians became incredibly influential in the Muslim world in the sciences, medicine, history, the arts, and literature. Iranians became some of the premier scholars of Islamic jurisprudence and were some of the foremost contributors to their own unique interpretations of Islam such as Sufiism. The assimilation of Turks and other Central Asian peoples into Iranian tradition further bolstered the number of Muslims in Iran. Iranian culture, in essence, became the catalyst for spreading Islam to the rest of the world. By the time we get to the middle of the 2nd millennium AD, all of of the dominant Muslim Empires in Asia were Persianate societies.
These are some major points. Iranian conversion to Islam was slow, and essentially very peaceful (though there are definitely recorded events of violence against Zoroastrians by Muslims). Please let me know if you have any questions as I did not get a chance to proofread this.
Sources: The Golden Age of Persia by the late Richard N. Frye
Zoroastrians: Their Practices and Beliefs by Mary Boyce
Wow I was honestly thinking of posting this exact question today! I'd also like to know if Persian citizens actually resisted the Islamic conquest and religious/political change?