Let's start with Judaism the original faith that kicked it off.
They were an insular tribe and seem to have absorbed concepts from other faiths into making a supreme deity into a monotheistic figure, though remnants of their earlier polytheistic culture can still be traced in religious texts. The key issue was they they kept their religion exclusive to themselves, hence the chosen people principle (which probably was a major political/social tool in their interaction with other tribes) One interesting feature is that while they do have religious texts a huge emphasis is put on debate, interpretation and consensus.
Christianity is a bit of a happy accident. It seems that around the early reign of Augustus one or more religious figures appeared in the Middle East and out of this emerged a new cult that focused on Jesus and did not keep it exclusive to a certain tribe or ethnicity. It was so radical that it quickly spread through the Roman Empire and although this was hardly the only such cult, it had the right combination of broad appeal and philosophy that it ended up being the official religion of the Roman Empire.
Now this new Christianity had to be established and the early leaders formed themselves into a religious community that operated inside society. Christianity holds a nominal difference between the church/pope and the state/Emperor. Now in reality the two were deeply interwoven, but this tiny gap had massive consequences. While historically the Christian faiths wielded great power and had influence over kings and emperors if only because they helped to seal their power, kings and emperors had the freedom to operate outside the church and often did have conflicts with it. Also the tenets of the fate have long been up for discussion and a near constant trend in Christianity has been the dichotomy between the power and actions of the church compared to the writings on which it is founded. And dissent is not foreign to Christianity on account of the split between Catholics and Orthodox churches, the various heresies and movements leading to Luther etc.
Come the printing press and Luther and the Jewish tradition of religious debate as well as a society where there is a religious and worldly distinction does lead to the first people to contend that religion itself might be up for debate.
So not only do we have an internal debate about which principles should be adhered to or the general discussion between Catholics and Protestants, but also internal discussions inside the Catholic faith itself.
And the major difference between the Catholic faith is that religion is seen from the institution of Rome, to them the bible is only secondary, their interpretation dominates.
Protestants will take the bible as their starting point and depending on their orientation interpret the bible in different ways, from strict literal belief to a more nuance approach where some elements are considered allegorical rather than historical.
As a result there was an opportunity for some people to start to look at the world without going through the lens of the bible to interpret everything. Science and Enlightenment started to look for naturalistic and humanist answers to the big questions trying to avoid religion if only to get another perspective.
It has been said that since Protestant denominations only have the bible as a guide they are tied to it when it comes to interpret things like the natural world. Whereas Catholic scholars who tended to consider the bible's claims as allegorical looked at the world and concluded that if the bible contradicted nature, but nature was ultimately god's creation and direct evidence in a physical form. That would explain why some people embrace creationism because the bible says so, while others embrace evolution because they think it can only be interpreted as God's plan.
Because the conflict between Catholics and Protestants caused huge problems mainly between the 16th and the 18th century we see an attempt to ease religious problems by allowing freedom of religion, and by making sure that no religious institution of whatever kind should have a dominant say in the affairs of the state. See also the US Constitution. Many European nations followed suit and today people have freedom of and from religion. A person is free to believe what they wish, but no religious group should try to force an individual to believe anything even if they make up a majority or claim they do have a say in all things.
Now that we have briefly highlighted two of the three major biblical faiths, we come to Islam.
It seems a similar process that happened to Judaism occurred around 600 AD in Arabia around the cities of Mecca and Medina. Polytheistic tribal cultures underwent a conversion to a monotheistic faith that may be based on a local lunar deity being expanded into an omnipotent being based on Jewish and Christian tradition.
And while I have described Christianity as a happy accident that was made up as they went along and ultimately settled for a Pope/Emperor model. Islam is extremely complete and detailed. Much more so than other faiths.
Now religions have often cornered the market on social behaviour with dictates and prohibitions. Islam also details aspects that are rarely touched upon by other faiths and often with much greater emphasis.
As a result Islam could be described as a complete package. If you ask any Christian they live in a mixed world, some aspects of their lives is of a religious concern, others are not. There is no such thing in Islam, everything is either regulated or claims to be regulated by it.
As a result if you ask a Muslim, they will answer to questions like what is your political system, your economic system etc with "Islam" everything is Islam.
A huge distinction as this means that there is a total assimilation of everything with Islam including the self.
Add to this the declaration that Islam is the final revelation, the final and most perfect form in which God revealed himself and his plan is now established once and for all and totally unchanging. Another critical point is that Islam describes that the first three generations starting with its founder were the best ones, so there is this kind of belief that the Golden age has already passed and the only thing one might aspire to is to emulate this Golden age as much as possible.
If God's plan is unchanging their is no debate. There is no room for interpretation other than some theological details. If Christianity has room to drive in a wedge of new ideas, this is not really an option for Islam. Whereas Judaic studies will look at every possible permutation with a certain level open-mindedness and the possibility of reaching a new conclusion, Islamic studies tend to look for the most orthodox interpretation of any given theological point of discussion and reinforce the commandments of Islam.
From a broad point of view what we have seen up to this point are merely variations and differing world views. In general they have little impact on how a society functions.
We find that all societies at some point have their transgressive moments be it an expansionistic phase through war and invasion of others, be it internal persecution of certain religions, ethnicities etc. Or even religious-inspired conflicts like the Crusades.
However we can find next to this periods of relative social peace where a nation is not under any threat and the focus is on internal development be it political, economic, religious, scientific etc.
Christianity and Islam both went through similar phases. Islamic scholars did extremely well in the middle-ages and early modern period, while Europe had a huge boost starting with the Renaissance almost until today.
What we have seen is that the nations of the Middle-East which for nearly a millennium were a dominant power in world affairs are now lesser players. Europe and company went through a development unmatched by any other power before it and became dominant in world affairs.
My own hypothesis is that starting around the time that the Ottomans took over as the main power and today, there has been a current inside Islam that has opposed any form of change. While I do not believe that it was probably not written with that intent in mind, the entire structure of Islam seems almost ideal fertile ground for enterprising authoritarian figures to control people into certain beliefs, much more easily than other faiths because there can be no resistance, no debate, no nominal line in which a dissenting voice can exert sufficient power and authority to turn it back.
I would therefore say that Islam is not the problem, but the way it is set up the the way it sees society is a huge benefit for those of a malevolent mindset. Most Muslims have lived in peace for all of history, just like most Christians never did anything wrong, but in an increasingly polarized world it's never been easier to play on the minds of so many people in such a terrifying manner.