Ah ha! I figured it out:
Under the 1906 constitution, Iran is REQUIRED to provided 5 seats in parliament for “religious minorities” in the country. This amounts to 2 seats for Armenian Christians (one for northern Iran and one for southern Iran), 1 seat for Assyrians, 1 for Jews, and 1 for Zoroastrians.
Surprisingly, this provision was retained after 1979 Iranian Revolution. (Maybe it would be have difficult and time consuming to abolish it?)
In any case, the lone Jew in the Iranian parliament is Homayoun Sameh (elected? appointed?) in 2020.
Most of these “religious minority” members appear to be token appointments who tow the regime line. The previous Jewish member of the Iranian Parliment, Siyamak More Sedgh, is on record saying that Israel is a corrupt “Zionist regime” that he personally dislikes. (However, another previous Jewish member of the Iranian parliament DID criticize the President of Iran for denying the holocaust)
https://en.wikipedia.org/wiki/Iranian_Parliament_religious_minority_reserved_seats
Saudi Arabia does indeed have zero Jews in their parliament, HOWEVER, they also have ZERO MEMBERS of Parliament, period. There is NO legislative branch there — all decisions are made by the Saudi Royal Family.
In short, its untrue to say that other Middle Eastern countries have “zero” Jews in government. However, it’s probably accurate to say they have zero Jews in a position of actual power.
I think its also accurate to say the Israeli Knesset frequently has ZERO Christian members (sometimes 1 or 2 at most), and (currently) the lone Christian is only “Christian” on paper. However, given that Christians are only 2% of the population, I’d say this is more due to the Christians in Israel being inept at actually getting elected, or working together in any meaningful way to influence government.
They got an entire new constitution in 1979. They probably kept the provision as window dressing.