The Saudis and Iranians are actually competing for influence within the region so there's little prospect of them working together. It's a Sunni v Shia conflict at its most simplistic.
Thats why I brought Pakistan into the equation, around 1974 or so they amended their constitution to define what is a Muslim and picked a side that is not compatible with western values and never will be.
Politicisation, militarisation and polarisation
Pakistan’s internal diversity within Islam led to sectarian contests over who was and was not a Muslim. As early as the 1950s, there were anti-Ahmadi riots spearheaded by Deobandi groups, in particular the Jamaat-i-Islami and Majlis-e-Ahrar.
In 1974, however, the Deobandi ideology prevailed in parliament. Only a year after the Constitution of 1973 came into force, the legislature passed an amendment to the Constitution, declaring that people who believe in prophets after Prophet Muhammad are not Muslim. One sectarian version of Islam had thus managed to impose its world view on the constitutional order. Because Pakistan’s president and prime minister must be Muslims, Ahmadis have since been excluded from these offices.
Things got much worse when, in 1977, General Zia-ul-Haq toppled the civilian government in a coup and suspended the Constitution. Soon after, with the start of the Afghan war in 1979, billions of dollars worth of military aid began pouring into Pakistan from the USA and Saudi Arabia. The goal was to resist the Soviet invasion in Afghanistan. In the process, Zia set the country on a “jihadist” path.
Deobandi and Salafi Madrassahs (religious seminaries) proliferated and became more radical. They were sponsored by the state and benefited from Saudi money in particular. These Madrassahs were integrated into mainstream education to train, recruit and mobilise Islamic fighters called the “mujahideen”, who joined the insurgents in Afghanistan. The military regime’s policies facilitated an arms and drugs trade across the border, and silenced the opposition at home through despotic laws and harsh repression.
To more firmly establish his power, moreover, Zia “islamised” various laws in a way that reflected an extreme and rigid version of Deobandi doctrine. All Muslims who did not subscribe to rigid religious fundamentalism – the majority – were thus legally reduced to a minority status. Moderate Sunnis as well as non-Sunnis had no choice but to be regulated by these harsh laws. The only exceptions were “personal laws” concerning private matters like inheritance, marriage and divorce et cetera. All religious groups, whether Muslim or not, were allowed to apply their traditional rules to these matters.
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You can see that this poses a serious threat to the west and the UK in particular given the amount of immigrants we not only allowed into the country from that area, but the practice of their returning "Home" or sending their children for extended visits.
So while the common belief is this problem remains from the middle east its far more complex.