Imagine that there is an unexploded bomb or mine or some such buried in your back yard. You know you must walk carefully to avoid triggering an explosion, that the bomb might go off by itself, or that the brat next door might chuck a stone over the fence, blowing up your yard.
Most Muslims are good people, but they follow a religion that explicitly calls for the extermination of non-muslims. Fortunately almost everyone is more moral than their religion, so that is rarely a problem.
However, the chance of an explosion is always there. For example when the metaphorical brat throws a cartoon over the metaphorical fence, the result is an explosion of threats, murderous riots and killings.
How can Muslims allay the suspicion of themselves that this situation produces?
1) There is nothing in the Qur'an or authentic hadiths that says Muslims should exterminate non-Muslims.
2) Your analysis of religion is simplistic. By the same token that lets you say, "Almost everyone is more moral than their religion" based on supposed bad teachings, we can say, "Almost everyone is less moral than their religion" based on the good parts of religion.
I find religion, including Islam, to be a complicated mix of good, bad, and everything in between. One-dimensional arguments don't hold much water in the face of reality.
3) Muslims can allay this suspicion the same way atheists can allay the suspicion of anti-atheists that all atheists are immoral, perverted individuals or the suspicion of anti-Jews that all Jews are conspiring and nefarious people: by pointing out that over-generalizations and simplistic thinking are intellectually bankrupt on a fundamental level.
Islam is not a monolithic entity, nor are Muslims uniform in what they believe about social, political, or even religious issues. There are Muslims who disagree with the average Muslim more than they disagree with the average European or American atheist.
Life ain't simple.