Today I found out about Kish Island, which has different visa policies to mainland Iran. Do these differences extend to allowing Israelis, who aren't otherwise allowed into Iran?
As an Israeli passport holder, it seems you cannot visit Kish.
According to Wikipedia:
Admission is refused to holders of passports or travel documents containing a visa/stamp for Israel or any data that passenger has been to Israel or indication of any connection with the State of Israel.
It also says:
All tourists may stay in Kish Island for 14 days or less without obtaining any visa. (Source)
But that is for tourists and people already in the country (Iran) who have obtained the visa. But since Kish is already in Iran, an Israeli passport holder cannot visit the place.