I think you should probably read or listen to what some of the Iranian leadership actually says about Islam, because it's pretty damn clear they have the same general world-conquering "unite everyone under Islam" ambitions as extremist Arab-Muslims.
And, as I pointed out, they're a wee bit hampered by the religious divides within Islam itself. Iran and Saudi Arabia have as much chance of uniting under a pan-Islamic umbrella as Utah and the Vatican have of uniting under a pan-Christian umbrella. The Iranians don't want to spread Islam if it means Sunni Islam (and, likewise, the Sunni Islamist groups don't want Islam to spread if it means Shia Islam).
They
may align in the short-term to face a "greater enemy", but even that isn't always a given (as shown by the Saudi government preferring to side with the US against a nuclear Iran).
I also have to question the argument that Iran's alignment with Nazism is solely a result of nationalistic and militaristic goal, and has nothing to do with religion. There are wide-ranging links between Nazism and Islamic Fundamentalism throughout the Islamic world, not just amongst Iran's population.
That has more to do with anti-Semitism. That is, the common ground between Islamic Fundamentalism and Neo-Naziism is not based on a shared religious interpretation, but in common geopolitical and some very specific ideological goals.
There's a clear link between the religious ideology and the political. (In fact, if you'll recall, under Sharia systems like in Iran, religion and politics are one in the same).
Yes, I admit that the admixture of religion and state in most of these Muslim countries makes a direct separation of their various goals and ideologies difficult at best. But it should also be said that there's no one
shariah, and that the combination of religion and politics in Iran is not the same as it is in Saudi Arabia, which is not the same as it is in Egypt. The contrasts are far more informative in this regard than the similarities.
And, as I also noted, specifically in Iran's case, there's a history to its authoritarian ethnosupremacist ideology that far predates the
veliyat-e faqih of the Islamic Republic of Iran, and especially in the early years of Iranian nationalism (the mid 19th century to the early 20th century) it centered almost entirely on the Persian and Iranian identity and culture as distinct and superior to even their fellow Muslims who were
not Fars/Persians. That ethnic identity, language, and history was
far more important to the Iranians than their religious identity.
In other words, when Reza Khan embraced Hitler's Naziism, it was because he felt the Iranians were to the rest of the Middle East and West Asia (Muslim and non-Muslim alike) what the Germans were (or, rather, considered themselves to be) to the rest of Europe, not just because of a similar racist authoritarian militarism, but because of the shared "Aryan" self-identification. It wasn't "We're following you now!", but "Hey, we both came from the same place and are going down similar paths!"
And that attitude has lasted even through the 1979 revolution (though the "Aryan" thing has diverged so that Iranians and Nazis no longer refer to the same thing when they talk about it).