I think Matt Duss hits the nail on the head here:
This, also, is part of what I think makes America unique: “Assimilation” has never been a one-way street. New arrivals to America have adopted American ways as their own, but they've also changed the way that we define and understand what it is to be American. Resistance to this is, I think, a big part of what underlies much of the opposition to the Cordoba House: Many Americans' are uncomfortable with the fact — and it is a fact — that America will become, is becoming, more Islamic.
I think this is broadly correct -- every new wave of immigrants brings with it anxiety over the way immigrants change American culture. In that sense, the fears of those afraid that Muslims will change American society are "justified" -- just like every cultural group has before it, American Muslims will make America a little more Islamic even as America makes them American. One of the amusing things about New York City, for example, is how many superficial cultural aspects of American Jewry it maintains -- from getting the High Holy Days off from school to the fact that you can get a bagel with lox at a bodega in Soundview. So in places like Michigan, with its large population of observant Muslims, we're going to see more midnight football practice during Ramadan. It doesn't mean imminent nationwide application of Taliban-style Sharia law.
There's nothing wrong with this; it's an old American story, and for those immigrants and their children who come to America voluntarily, it almost always has the same happy ending. The reason is because they want to be Americans -- that's why they come here in the first place.