So, Roger, if one is seeking for doctrinal evidence, as you did in pointing out the reply Jesus gave to his questioners of giving unto Caesar what is Caesar’s as the clue to the basis of Christianity’s eventual reform, it is not hard to find in the Quran what points to moderate Islam. But the problem is embedded in history and not in the text, whether it is the Bible (Old and New) or the Quran. The problem is with Muslims as people and how they read, understand, and practice Islam — and how they also understand the world in which they dwell.
I read the same text, the Quran, just as I read the text which is the world itself in historical time, and I share nothing, or not much, in my reading of both with the men who flew aircraft into the World Trade Center. Nor do my reading of the Quran and my belief as a Muslim have anything in common with Islamism, the ideology that motivates Muslim or Islamist terrorists, their ideological masters, and their apologists run amok in our world. Your question about moderate Islam is a political question and not a religious one, if we keep in mind the distinction between politics and religion. The pre-modern or ancient world did not make allowance for this distinction, and the vast majority of Muslims has not made the shift from the pre-modern to the modern world.
Religion and politics were inseparable in history until the separation occurred — a separation which was institutionalized in the making of the modern world with Europe as its cradle. The experience of living in society with religion and politics held apart, as in the United States, is merely a blip in time. The fusion of religion and politics meant that the dominant faith of a people was also the instrument of political legitimation for the state and its rulers. This remains so in many parts of the world — particularly in the Muslim world. It was true when Judaism was the ruling creed of the ancient kingdoms of Judah and Israel, when Christianity was the state religion of the Holy Roman Empire, and today in contemporary states where Islam is the state religion — Iran, Saudi Arabia, etc. I am reminded here of the words of Albert Camus in The Rebel: “Politics is not religion, or if it is, then it is nothing but the Inquisition.”
From the modern standpoint, to ask whether Islam is moderate is to question the nature of politics in the Muslim world, and how this politics encloses Islam as religion. Observe the practice of Islam in Afghanistan, Pakistan, or Gaza, for instance, and you conclude that Islam ipso facto is immoderate. But that would also mean that Muslims in these places generally, or in sufficient numbers, are by their nature immoderate people.
By the same token, observe the behavior of Muslims in Europe and North America who apologize for of Islam as practiced in the manner that is outrageous to modern sensibility (from gender exclusion to persecution of minorities to preaching violence against dissident Muslims and jihad against infidels in the West, Jews and Israel, and Hindus in India), or the outrageous behavior legitimated by appeal to the Sharia or Islamic legal code, and non-Muslims might well — indeed, should! — conclude that such apologetics illustrate the immoderate Islam of immoderate Muslims.