Not all Muslims hold beliefs on Sharia which conflict with Democracy.
Some Muslims believe that in Non-Islamic states, Sharia is for religious matters. An sloppy, poor analog to this would be modern Catholic tribunals, which hear matters of annulling marriages, reconciling excommunicated Catholics, etc. In such a matter, a Sharia court would only have legal weight so far as the parties involved choose to “play along.” For instance, Catholics denied annulments can still get married again in the eyes of the state.
Some Muslims believe that Sharia’s intent was for Muslims to adopt the culture of the societies in which they found themselves, except their religious practices.
And many, many Muslims are what Christians would call “nominal.”
"March 5, 2007 8:23 pm By Robert SpencerReleased by the delegates to the Secular Islam Summit, St. Petersburg, Florida on March 5, 2007
Having pondered the creation of what appears on the surface to be a laudable attempt to create a moderate Islamic movement I'm still hesitant to support.
My reservation/concerns about this movement is it will likely mirror the destructive forces of the secularized Reform Jewish movement - aka the hard left.
Much of the damage to society comes from the 'anything goes' progressive secularization hydra of societal destruction.