Do note that I'm looking at this from the historical perspective...
@Ntwadumela could talk about the religious perspective and correct me if I've muddled up my history. Many of the works that talk about this history are translated from Arabic and I don't speak Arabic...
I would argue that the main problem (or benefit, depending on how you look at it) is that Islam is a very decentralized religion, there's no spiritual governing body. There's no diocese or bishiphoric structure in Islam. Mosques can preach what they want, and there is no formal religious body that makes the rules. (Historically, it's been the Caliph as the nominal religious head). The split for the Sunni/Shia is over who should have succeeded Mohammad as Caliph, the Sunnis say that Mohammad never named his successor and later, the faithful convened to give the title of Caliph to the Prophet's father in law, while the Shias say that Mohammad named his successor, his cousin, as the nominal religious head. It started as a political schism and later grew into a religious one.
Historically since the Shia were a religious minority, under a very hostile regime they had to figure out a way to survive. This led to the concept of Taqiya, where a Shi'ite can falsely confess their faith in order to better serve the religious community, sabotage the enemy and to survive. The Assassins(yes those assassins) were very fond of this tactic and used it to great effect to assassinate Conrad of Monteferat and to convince Saladin to stop sieging their stronghold
There is also a sect of Islam called the Ibadis. They're mainly located in Oman. If I'm reading this translated article right, they believe that only God can annoit a Caliph.
Oftentimes, this meant that the direction the religion took was often up to the person or family who held the title of Caliph. The Abbasid Caliphate who took over the nominal title of Caliph after a war with the Umayyad Caliphate, were kind of nuts, and if you have an afternoon, the stories of political intrigue and court politics in the Abbasid empire makes for a fascinating read. I'm talking sons being strangled by the mother of another son. That kind of stuff. The Abbasids later collapsed thanks to this court intrigue and lost large portions of their empire to the Shia Caliph under the Fatamids in Egypt.
The Fatamids were later succeeded by the Mamluks, (now, we are back to Sunni rulers) a term meaning slave soldier, but later grew to designate a social class very similar to the European Knight.
The Ottomans later overran Mamluk Egypt. After that, came the Ottoman Caliphs as the nominal religious head. They interpreted Sharia law to mean "we can make religious rules in our empire for Muslims, non Muslims will be subject to the religious rules laid out by their own religious heads" This system was called the Millet system, and it was an insanely effective form of early religious pluralism.
Unfortunately, near the end of the empire, they did marginalize their religious minorities, although it isn't known whether this was an expression of religious dominance or Turkish dominance, as religion in the Ottoman Empire was generally seen as a very "personal matter."
Finally, we come to Saudi Arabia. Their interpretation of Islam is called Wahabbi. "Conservative" doesn't do this ideology justice. It's fundamentally reactionary and hostile to not only Shias and non Muslims. It's hostile to more liberal interpretations of the religion as well.
The Saudis under Wahabbism have bulldozed significant places in the Prophet's life, and also have bulldozed Ottoman structures in an effort to change the historical narrative. They invest a staggering amount of cash in funding mosques to replace Sunni Islam with their own harsh interpretation of the religion. This is especially problematic because Saudi Arabia controls both Mecca AND Medina, and as such, they can exert a large amount of indirect pressure on the religion.
Unlike the ways the Ottomans interpreted Sharia, there are no room for the Dhimini(people of the book) in a Wahabbist society. Everybody who is a citizen of Saudi Arabia, MUST be a Muslim.
I wouldn't say that the religion needs a total reform, but we need to find a way to work with and promote "Liberal" clerics within the religion,
Start by not letting Saudi Arabia fund mosques in your country...
