One reason might be that Sharia law and the United States Constitution cannot coexist since Sharia law is incompatible with our Constitution. A further reason might be that ultimately Islam would, therefore, lead to the advocacy of the overthrow of our governments by force and violence since Sharia law is filled with unconstitutional violent punishment for all who do not conform to it, which our institutions could not do without throwing out our Constitutions, state and federal.
That's it in a brief sentence. Americans don't really make a lot of assimilation demands, in language, dress, music, diet...but we do demand one thing: that the Constitution be the law of the land and supersede any additional legal codes that may come with the culture. Cultures where that is impermissible will not get along here. Cultures intent on subverting it, from Communism to Islam, will be resisted as the enemies they have proclaimed themselves.