Ever heard of Saddam Hussein? Yeah, he was a murdering fool. His murders were directed solely toward moderate and liberal Muslims. Saddam was a fundamentalist Muslim, much like Pat Robertson is a fundamentalist Christian. Saddam believed that the Koran was entirely true, and so it was his duty to kill apostates and moderates, and infidels.
Moderate Muslim's may not be moderate enough, however. They still have a hard time embracing the ideas of Americanism. This is probably why many in the west are not ready to open their doors even to moderated. It may take many more decades of propaganda and enlightenment to help Muslims see the ideas of freedom and common law for everyone.
Moderate Islam is the form of Islam that we see in most western BORN muslims that are content to live in their own religion and don't often interact with others of the community and can live side by side with western views such as the LGBT communities. Unfortunately this is not the mainstream Islam the mainstream Islam is the majority population that controls the governments of the middle eastern countries. This is the culture that is the poplar opposite of our own this is the culture that regularly executes people for their beliefs such as being part of the LGBT community.