I know that whenever I want to understand a foreign culture, religion, or political structure, the first person I think of asking is volfanjustin.
You should go to those who have actually studied and experienced their religion from the inside then come out of it.
The "estimate" that is often bounced around is that about 10% of Muslims agree with the more extreme views of jihad. About 1% are actually radical enough to become "soldiers"... the problem is that amounts to an army of 10 million.
Worse yet, most of the supposed moderate 90% aren't convicted enough to stand up and stop the 10%.
A fundamental, Koran thumping Muslim... is more likely than the avg Muslim to be a violent extremist. A fundamental, Bible thumping Christian is more likely than the avg professing Christian to be law abiding and non-violent. NT Christianity teaches spiritual "warfare" by persuasion using the weapons of love, peace, charity, goodness, morality, etc. A NT Christian is willing to die for his faith but not kill for it. The Koran teaches that violence is a legitimate option for spreading Islam and suppressing infidels. A fundamental jihadist is willing to both die and kill for his faith.
The biggest problem with liberals and the west generally is that our paradigm says that there is separation between religion and politics. Though liberals go to radical extremes, we very much have that separation in the US. Few advocate supporting churches directly through taxes or adopting church doctrine as law. Religion certainly informs the political views of individuals which is completely legitimate... but no one is trying to establish the type of church-state relationship the USC addresses.
Islam is thoroughly theocratic. There is no distinction or separation. To separate political from religious objectives is antithetical to their worldview.
We are failing to assess a very real political threat because it is clothed in a religion that has a large number of benign followers. But there is no question- the political acts of Islamic countries and terrorists are ultimately in agreement with Islam's doctrinal belief that it must rule the world.