Nasir al-Mulk Mosque in Shiraz, Iran
What happened is that after Umar ibn al-Khattab RA was killed a country-wide revolt erupted in Persia and also the new Caliph, Uthman, RA sent forces to subdue the rebels. The revolt was particularly brutal in some urban areas, which had a devastating effect on the civilians.
It is during this phase of the conflict that an unknown number of Iranian civilians were killed. However, their deaths, whilst unfortunate, doesn't constitute religious persecution since they weren't killed for his or her faith rather for getting caught within the fighting between the rebels and Arab army. Although admittingly, some Zoroastrian priests (Parsis in pakistan and india) were intentionally killed.
Even still, overwhelming majority of Iranians weren't Muslims after the tip of the revolt and Persia would remain largely non-Muslim for a pair of centuries.
But how did Persians convert if Arabs didn't convert them? It's simple; they converted themselves. Direct Arab rule out Iran only lasted for 174 years then Iranians gained autonomy. During this era, Arabs made no attempt whatsoever to forcibly convert Iranians. That just never happened. [1] (Apparently the regional governor Al-Hajjaj bin Yusuf did attempt to convert some Iranians by force).
As to the jizya tax propaganda, it's been debunked several times by now. Jizya was a tax levied on fighting age men as a substitute to conscription. Children, women, poor and clergy were all exempted from paying it. [2]
Although the Umayyads did try and force Arabic on non-Arabs by designating it because the only language of administration, nobody was forcibly converted and also the Iranians would later help another rival dynasty, Abbasid, to succeed in power.
After gaining autonomy and later full independence, the native Saffarid dynasty set about converting Iranians to Islam. That explains why the Islamization process of Iran was relatively faster than in Egypt and Syria, because these areas weren't ruled by native dynasties unlike Iran.
This is demonstrated in Richard W. Bulliet 's graph of conversion to Islam within the medieval era [3]
As you'll be able to see, most Iranians converted within the autonomous period under the Abbasid Caliphate or during the rule of independent native Iranian dynasties.
Iranians would persist to convert the Turks and therefore the inhabitants of the Indus Valley to Islam.
In fact, the foremost important scholar within the history of Sunni theology was Iranian! His full name was a. Abū Ḥanīfa al-Nuʿmān ibn Thābit b. Zūṭā ibn Marzubān or simply Abu Hanifa. He's the founder Hanafi school of Sunni jurisprudence which is that the most generally practiced school of law in Sunni tradition.
Resting place of Imam Abu Hanifa, Baghdad
One of the 2 most authentic hadith collections was gathered and compiled by an Iranian called Imam Muslim bin Al-Hajjaj. the opposite one was also a Persian but from modern-day Uzbekistan. These are just two of examples out of the many Iranians contributions to Islamic theology. does one think Iranians would have done such a lot to Islam if they were indeed forcibly converted? If you are doing then you're mistaken as history proves otherwise.
And that's only for Sunni Islam. Shia's theology is whole another history. The mythical narrative of “Arabs converting Iranians by the sword” lacks evidence then it remains because it is, a myth that ought to be enamored a grain of salt.
Footnotes
[1] The Golden Age of Persia
[2] A History of Islamic Societies | education from university Press
[3] Islam
Finally??