I have dual citizenship: Polish & American and reside in USA. I have an Israeli stamp in my USA passport, so I don't want to use it as I heard that would not be allowed. I would like to travel on my Polish passport, but will that raise questions regarding my USA passport as I reside in the US? Or perhaps additional questions on which countries I travelled to on American passport, etc.
Due to the rules dominating over Iran, entry to Iran will be refused to citizens of Israel and travelers with any evidence of visiting Israel. Israel is the only county included in this rule and other countries even America are excluded.
On the other hand, the American visitors of Iran should take part in a guided tour to travel in Iran. It takes about 30-45 days to secure visa reference number for Americans. After having the reference number, the visa can be collected in two working days by direct referral or in one working week by posting the docs to the Iran embassy. So it is better to use your other passport which makes no problem for you.
For more information about Iran visa and filling the application form follow this link: Iran visa