Moses was also an iconoclast.
Do Jews have icons for "GOD"
Biblical 'Old Testament' Judaism was very similar to Islam. In part, that's because both of them arose from Semitic-speaking recently-nomadic peoples who shared similar cultural practices and worldviews. And partly it's because Mohammed based his 'revelation' on Judaism and its mythology. Islam is basically a restatement of early Judaism, re-making it the way Mohammed wanted it to be. (Muslims would insist that it's the way God wanted it to be. Mohammed just channeled the eternal heavenly Quran, he didn't compose it himself.)
Islamic Shariah is very similar, point by point, with the Jewish law found in the books of Deuteronomy and Leviticus, found in every Christian Bible.
But Judaism and Islam experienced very different histories subsequent to their early tribal legalistic stages. The Jews didn't typically try to conquer their neighbors. They held themselves aloof from and superior to everyone else, imagining themselves as the world's race of priests, intercessors with the One God, called to maintain a special ritual purity. They spent their time trying as hard as they could to keep their tiny states from being overwhelmed by the Assyrians, Babylonians, Egyptians, Persians, Greeks and Romans surrounding them for a thousand years. But if somebody today could look inside Israel and Judea during Old Testament times, what they would see is something not dissimilar to the what Islamists dream of for Islam today. A theocratic state governed in principle if not practice by a crudely conceived divine law.
The collision with the Romans resulted in two devastating wars, in roughly 70 CE and 130 CE. The Jewish state was totally destroyed, and the Jews were exiled from Judea and Jerusalem. Their Temple and its priestly hierarchy disappeared.
So a new pattern evolved in Judaism, one that lasted for 2,000 years down to the present. Jews were religious minorities in other people's countries, scattered around the world's cities in Medieval and Modern times, living in small communities grouped around their Rabbis and their local congregations. Far from being able to enforce their Law on others, they were subject to discriminatory laws that others directed against them. So necessity forced Judaism to become a personal and private religion, instead of a legalistic system of theocratic organization for societies as a whole.
Islam's trajectory was entirely different. In just a few years after the death of Mohammed, the Arabs, fired by the excitement of being on God's invincible side, surged out of Arabia and conquered the entire Sassanid Persian empire and half of the East Roman/Byzantine empire. Within a single generation, their rule, and their Law, extended from the Atlantic coast of Morocco to the Indus valley in India.
That initial success, to theunprecedented in all of human history, has shaped Islamic sensibilities ever since. It's what drives Islamist Jihadism today. The tribal Arab bedouins who surged out of Arabia during those years were culturally far more backward than the much more sophisticated peoples upon which they imposed Islamic rule. The one thing that the first Muslims had going for them, the thing that made them invincible, so today's Islamist historiography goes, is their single-minded loyalty to the revealed Will of God.
But inevitably Muslim rulers appeared, who faced with the challenges of administering a real life state, started compromising, learning from those they had conquered and established secular administrations. Soon there were kings and royal courts and wars conducted to further the interests of those kings, not the interests of God. Regionalism appeared in the Islamic Ummah, as ambitious local officials established themselves as kings, and the Unity of the early God-favored Caliphate fragmented into the plethora of ostensibly Islamic nations that we see today. They fell prey to theological disputes such as the Sunni-Shia divide and to the skeptical corrosive influence of Greek philosophy.
And as the unity and single-minded enthusiasm of the earliest Muslims faltered, the tide of invincible Jihad ceased. The Islamic world found itself on the defensive, against the devastating attacks of the Mongols, the less important Crusades, and most overwhelmingly, against the obvious superiority of the modern West, powered by science and the industrial revolution.
Islam is a proud culture, as convinced as the West is of its own superiority and its inherent destiny to transform the planet in its own image. Islam's inferiority to the West with its science, engineering and rationalism was hard to take. So Muslims searched desperately for ways to make things right, for ways to restore Islam to its rightful place.
Islamist historiography insists that Islamic history itself reveals the answer. The word 'Islam' means 'submission' (to God's will). As long as the early Muslims were totally devoted to God's will, God was alongside them and nothing could stand before them, however advanced and sophisticated it might be. But as soon as people started thinking for themselves, as soon as they started putting their own ideas, goals and purposes in the place of God's, everything started to fall apart.
The social-change prescription is obvious. We see it most clearly exemplified by ISIS. The restoration of the 'Caliphate' and the call for all Muslims to acknowledge it. ('Caliph' was the title of the leader of the unified Islamic community after the death of Mohammed.) The savage punishments. (Their loyalty is to God's Islamic law, not to human ideas of ethics.) The initial rush of success last year, when they took Mosul and 1/3 of Iraq, with almost no resistance.
They are consciously trying to return life and human sensibility to the way they imagine it was in the 7th century, Islam's moment of glory.
I think that less extreme versions of the same Islamist impulse are visible today throughout Islam. Women are far more likely to wear hijab-scarves (symbolizing that they are observant of tradition) than Muslim women were a generation ago, when more seemingly wanted to show off their modernity. Islamic jurisprudence (and the Law upon which it is based) has a correspondingly higher status today than it did when it was viewed as a vestige of an outmoded past. Muslims everywhere seemingly believe that Islam needs to be strengthened, and that the way to do that is to grasp ever tighter onto what are supposed to be the fundamentals of their tradition. They imagine that individual Muslims and Muslim society will be much better off when that happens.
Islamism can perhaps be interpreted as the rebellion of a medieval world sensibility against the historical changes wrought by the rise of the modern world.