Look at it another way:
AQ and MB are DEFINITELY Islamic & Islamist.
Mullahs, Ayatollahs et al, in charge in Iran, are “pro-Islamics”, and are “fundamentalists” too - even if they’re Shi’ites.
Iranian Ayatollahs also Actively support Sunnis & Wahhabis when it suits them. Look at Iranian regime’s support for the Palestinians for the last 3 decades - Palestinians are Still predominantly Sunni, not Shi’ites! So, why?!
Bottom line: AQ, MB and Ayatollahs ALL adhere to Islam.
But, Iranian Ayatollahs, mostly, give much more lip-service to Islam than AQ & MB do. Because Islam, Islamic/Arabic ideology, anti-West, anti-US stuff not only unites them with the Sunnis, but is, essentially, their bread & butter to hold on to Power & their Power base in “Shia” Iran. Even if that Power-Base is not the majority; they force it on the majority in Iran.
On the “majority in Iran” note, I believe the majority of Iranians, despite officially being Shi’ites, are not (mostly) moslems; neither culturally, nor in their practices. At best, the majority is very confused, and has been rightly frightened over the decades, due to forced, misleading religious education, as well as fear for their lives & livelihood. Emphasis on “forced”.
The UK, France, and the US, OTOH, over the decades, have simply supported Islam (Shia or Sunni). Politically, Socially, and Culturally. They’ve have let it permeate throughout, East & West. Especially as it suits their own agenda.
All in all, not a very complicated matter. But, more deliberately convoluted by all parties involved.
Keyword is ISLAM, itself.
Islam ultimately unites against “infidels”, does not divide the Islamists, who have their own agenda. They capitalise on & pride themselves on having indoctrinated entire countries & people.
You are right and wrong as well.
Most Iranians/Persians are Muslims and not confused at all about it. However, prior to the dictatorship, and 30+ year reign, of the Shia theocrats in Iran, the practice of Islam with most Iranians/Persians were (1) not evangelical (seeking to “advance” Islam around the world) and (2) not fundamentalists; but truly ‘moderate’ Muslims with more of a ‘live and let live” attitude towards non-Muslims and not ‘puritanical’ judges againts their fellow Muslims.
But ‘most’ Iranians today are under the age of 25 and have grown up entirely under the theocrats knowing very little of Islam outside of what the mullahs have permitted them to learn.
While voting majorities unleasshed from the strick controls of the theocrats in Iran, on a few occasions, have shown their willingness to reject the political monopoly of the theocrats, it is not clear to anyone outside the Iranian people just what that means about their interpretation of Islam today. It is certainly not clear that the ‘democratic’ movements in Iran against the theocrats represents any outright rejection of Islam.
You are correct that there are many ‘fronts’ across the Middle East with many alliances of convenience that cross the Shia-Sunni divide.
Those alliances are temporary and mere expedients.
The Shia-Sunni divide IS as old as Islam and it is fundamental to Shia and Sunni branches today. Even ‘victory’ against ‘the west’ will not close that divide. And while all those alliances of convenience are going on, the theocrats in Iran representing the Shia at their most fundamentalist and the Wahabi-Saudi-MB aliance representing the Sunni at their most fundamentalist DO believe THEY (each of them) are currently in a global war against each other, to become the ulitimate leaders of Islam and put that divide to rest by eliminating or silencing the other side.
It is for that that the Iranians are developing nukes - not for war against the west (unwinnable by any measure), and it is for that that the Saudis - more than anyone else in the world, want us or the Israelis to end that project. Frankly, they would prefer we NOT do it ourselves, because if we do it then ALL Islamists will miss another opportuntity for another reason to hate the Jews. If Israel does it then the Wahabi-Saudi-MB alliance gets the Shia theocrats knocked down a peg and Israel gets the blame. How convenient. So, if it HAS TO BE DONE, then from my view it should be the U.S. alone and NOT the Israelis who should do it.