Yes, Eid al-Fitr and al-Adha are celebrated in Iran but no way as big as in Sunni countries and Sunni regions in Iran. As a matter of fact, those two actual Islamic Eids have very little significance in the calendar of most Iranians, including religious Iranian Shiites (who venerate the innovated Ghadir al-Eid the most!). Both of those Eids are absolutely nothing and insignificant when compared to Nowruz.

All people and modern-day nations that celebrate Nowruz hail from the Iranian Plateau (and its bordering regions), a region stretching from the Caucasus in the north to the Persian Gulf in the south and from Eastern Turkey in the west to Western Turkistan in the east—a region that is sometimes called the Iranian Cultural Continent, representing the extent of the Iranian-speakers and the significant influence of the Iranian peoples through the geopolitical reach of Greater Iran.

It is thus no surprise that Persian Zoroastrian pre-Islamic customs can be found in these regions. Islam welcomes customs of different cultures as long as they are not opposed to Islamic principles (celebrating a Zoroastrian holiday under whatever guise is certainly condemned in Islam).

As for (some) Sunnis celebrating Nowruz: First of all, this is a blatant generalisation. In Iran for example, Nowruz has zero significance in the culture of most Sunni Iranians, especially the Iranic Baluch. Recent (and repeated and mainly failed) attempts to spread Shi’ism and Nowruz amongst the impoverished Baluch people are a testimony to that. As for the Kurds: Yes, some Sunnis Kurds in Iran and Iraq do celebrate Nowruz, however, you will never find a religious and knowledgable Sunni Kurd doing so for the simple fact that his sect (Shafi’i Sunni) doesn’t sanctify and condone this holiday. This is why you will find the irreligious and secularised folks amongst Sunni celebrating Nowruz (same in Afghanistan where Nowruz has little to no significance in the culture of the Sunni Iranic Persian-Tajiks and Iranic Pashtun Sunni people. It’s mainly celebrated by ignorant and deviant elements from within society such as irreligious secularists and Sufi type of people and of course the Shi’ites).

As for it being ‘merely’ a cultural holiday: The same excuse other secularists and ignorant folks bring up when they try to justify why Christmas is allowed to be celebrated (‘we just gather with the family in the winter holiday season’). Fact is, Nowruz is the main and most venerated holiday of Zoroastrianism. Watering it down to a cultural holiday won’t change its roots and origin and in Islam, all religious holidays have been abrogated and replaced with the two great Eids of the Muslims.

So the difference is simple and straightforward: (Some) Sunnis who celebrate Nowruz are opposing their religion (Islam) and sect (Ahlus-Sunnah) since neither have ever sanctified Nowruz whereas Shi’ism and its clergy regard Nowruz as a holy day and Eid, a big difference many don’t seem to grasp. I’ve met many naive Arab Shi’ites from Iraq to Lebanon who are not aware of this delicate difference, they still believe that Nowruz is just some cultural Persian holiday, not knowing that the evil Rafidi clergy has attributed it to the Ahlul-Bayt.  Little do they know that their charlatan Persian clergy, from Kulaini (over 1000y ago) to Majlisi II (16th-century Safawi palace scholar) to their modern day ‘Ayatollahs’ have sanctified Nowruz as a holy day on which the Shi’ite is encouraged (!) to perform numerous religious (!) acts of worship and on that day the saviour (fake Mahdi) will emerge to slaughter the Arabs with the help of the Jews and Persians.

Allahul-Musta’an