A dozen and a half years ago, when I visited Persepolis, the guide told us how the locals defeated the mullahs who tried to destroy the place soon after the revolution.
Yep, Persian are very proud of their history and culture, it has saved many sites
Following ajoszucs comment above "Iran and Saudi Arabia were quite harshly against the preservation of unislamic ruins and old cities, and now they put sites on the list every year
." I have been discussing the matter with a contact in Iran (who is not "pro" the regime). Indeed I think there is a large difference between the long term "anti tangible heritage" Wahhabi-inspired culture in Saudi - which held sway in the country until fairly recently and the events which took place during the "chaotic period" of the Iranian revolution - which never gained control of the country - even if Khomeini was often ambiguous in ihis statements..
Undoubtedly there is a "fundamentalist strand" within Iranian Shiism which, even today, tries (without a great deal of success!) to prevent statues of non Islamic persons being erected in Iranian towns. But Iranian religious culture has never demonstrated the total hostility towards depications of humans etc which has been common in many Islamic societies and reached an extreme in Saudi. Anone who travels around Iran will know that statues are everywhere!
The events at Persepolis were part of an anti Royalist rather than hard line Islamic movement - in the early days of the Iranian revolution anything with ANY connection to royalty was destroyed - anyone who has visited the the Sa'dabad Complex outside Tehran will remember the boots of Reaza Shah which are the only bit of his staute remaining! Any place with the name of "shah" was changed. And Persepolis was to be included because of its connections with Cyrus... and also of course with Mohammed Reza Shah who linked himself to the site via his OTT celebrations of 2500 years of royalty there in 1971. The incident was initiated by Ayatollah Sadegh Khalkhali, widely hated in Iran and known as the "Hanging judge".This article
gives quite a good indication of the nature of anti heritage actions in Iran during the Revolution, including the movement against Persepolis, and thereafter through to 2015.
Apparently the poet Ferdowsi raises particular dislike among hardline Mullahs - but statues of Saadi and Hafiz are ok. I am told that Omar Khayyam is a problem for them!!
Other examples given of the destruction of e.g historic Hammams in Isfahan seem to arise more from the more common human attributes of greed and lack of interest than from any deep seated dislike of "heritage". One man's "historic hammam" is another's "block on progress"!