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To be fair, there are verses in the Quran which are less extreme. What to do when there are some verses say this and some verses say that? The concept of "abrogation" is in force when it comes to the Quran. Later verses abrogate or supplant earlier verses. For more on abrogation: The Problem of Abrogation in the Quran. The more moderate verses tend to be "abrogated" by the more extreme ones, but those earlier verses are very handy for quotation by those minimizing Islamic extremism.
It is interesting to note that those earlier verses came from a time when Islam was new, militarily weak, and was itself being oppressed. For some reason, the Quran became more militant after Muhammed and Islam became militarily strong.
Some relevant links:
What if America treated Muslims in a similar manner to how Christians are treated in a Msulim country? Here are a couple of articles on the subject, both referring to the same source.
Non-Believers Under Islam
You have heard it said by many in the West that Islam is a "religion of peace." You have no doubt also heard that "Islam means peace." Those who repeat these lines are either ignorant, or perhaps they believe that such repetition might lead Muslims to become more moderate.
You might also have heard that a radical Muslim wants to cut off your head while a moderate Muslim merely wants a radical Muslim to cut off your head.
Of course, the truth lies somewhere in between. But first let us dispense with what Islam means. Islam means "submission." That is, submission to the will of Allah. Presumably, if all so submit, we will have peace - although the Sunni - Shiite division within Islam belies this claim.
Our focus will be: what is the status or role of non-believers living under Islamic rule? The following is probably the best short summary of Islam's view of non-believers.
The graphic above comes from an interview with Rober Spencer: Islam, Political Correctness, and Death to Infidels. It is well worth reading.
To a Muslim, a non-believer or unbeliever is a kafir. To a Christian, a non-believer is simply someone who is not a Christian. Kafir carries some connotations that go beyond simple non-belief. A kafir rejects belief, which is more active than mere non-belief. According to Political Islam, a kafir is a "concealer" - one who conceals the truth about Islam.