Although there are about 1.5 billion Muslims world-wide, Pew’s 2007 survey estimates that they only form .6% of the U.S. population. There are higher and lower estimates, but even the most generous only put Muslims at perhaps 2% of the population of the United States.
Unsurprisingly, most Americans don’t know a Muslim personally.
Islam is a diverse religion, and the sects can be at least as different as Catholics and Quakers. In terms of their view of the proper relation of religion and government, Muslim majority nations range from the fundamentalist and autocratic Saudis to a theocratic Iran that struggles with the conflict between that rule and the ideal of consent of the governed, to democratic Turkey, where strong secular ideals restrict the wearing of headscarves by civil servants in public buildings, which would probably be seen as a restriction of the free exercise of religion in the United States.
American Muslims in particular are not a monolithic phalanx of Sharia imposers. According to a 2007 Pew poll, only 50% think their holy book is the literal word of God: about the same as U.S. Protestants. 60% say “there is more than one true way to interpret Islam” 51% are very concerned about the rise of Muslim extremism in the U.S. 62% think life is better for women here than in Muslim countries.
It would be unjust and unwise to treat a U.S. mosque as a symbol of militant Islamic extremism; like treating the Christian cross is a symbol of clerical child abuse.