This reminds me of the term "Moderate Muslim". This term is used to describe those of the Islamic faith who disagree with Sharia law, jihad, and honor killings etc.. The way the terms "conservative", "moderate", and "liberal" are used today (great post by Steven), I would consider these people liberal muslims, as they don't seem to have much respect for the Qu'ran, as their "holy book" is quite clear on what should be done to "infidels".

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John 6:67-68: "Jesus said therefore unto the twelve, 'Would ye also go away?' Simon Peter answered him, 'Lord, to whom shall we go? thou hast the words of eternal life.'"