So let's say roughly 80% of Muslims have significant gaps in knowledge of the core teachings of the religion they profess to follow. You OK with that Spinoza? In other words - and correct my reasoning if you find it faulty - 80% of Muslims do not reject the violence and politics in the Koran as a matter of principle because they do not know about it.
That's faulty reasoning.
Some of the teachings in the Qur'an that they may not be aware of already contrast with principles that they have attained by other means. If they ever were to stumble upon a 'violent and political' interpretation of the Qur'an, they will likely reject it, or alter it to keep in line with their principles.
These Muslims have convinced themselves that numerous scientifically inaccurate verses in the qur'an are actually miraculous, and in the face of all evidence to the contrary they staunchly believe that it's so. They've re-interpreted the qur'an's faulty and out-dated science to fit modern times, they can do the same with its politics.
What proportion of that 80% would you reckon are devout insofar as their understanding of Islam goes and consider themselves good Muslims in the sight of Allah?
Insofar as they consider Islam to be about being the best person, from a moral viewpoint, they can be (in senses that are mostly sound), I'd say less than half.