My wife and I are thinking about traveling to Iran in the fall. Potential Visa obstacles: 1) I work for a television station - no big deal, I can just say I'm retired, right? 2) I'm Jewish. No big deal, right? 3) I have an Israeli visa in my passport. Do I need a new passport? 4) My wife is an ordained member of the (non-evangelical) Christian clergy. No big deal, right? Finally, we're looking for a guide/driver who is articulate (in English), patient, knowledgeable and able to get us a bit off the beaten tourist track.
1. Working for a television station doesn’t imply that you're a journalist. It is better not to mention anything related to media or journalism!
2. Being Jewish isn't a problem since there is a Jewish community in Iran. It is Israel that Iran has issues with, not Jews.
3. Due to the rules dominating over Iran, not only Israeli nationals are not allowed to enter Iran but also the travelers to Israel are not authorized to get a visa to Iran while they have Israeli visa stamp in passport. Israel is the only county included in this rule and other countries even America and the neighboring countries to Israel are excluded of this rule, it means that having the visa stamp of those countries is not a barrier to get authorization of entering Iran.
4. Your wife shouldn't have any problems declaring her profession. Clergy person is ok but preacher is not. So as far as she is a not a preacher she will not face any problem in obtaining visa.