We are a bit off-topic on this thread. Hardly every happens, right?
Having said that, I think you are at the core of the immigration issue—people are fearful of the cultural changes going on in America. More people from different cultures (e.g. people of different races or Muslims, or more generally anyone not like them or with foreign values) threatens their image of America.
Here’s the problem I see—America has always been changing. It is the essence of the “American experiment”. And the experiment is on-going—ever changing and ever challenging our view of ourselves. This will not stop—if it does, then we no longer free, and in my view we will no longer be the America that our founders conceived. Liberals tend to embrace change from an egalitarian viewpoint, and conservatives tend to promote our traditional social institutions in the context of our existing culture (or go back to a past cultural context—a reactionary view). So, can we find common ground?
Actually the problem is your lingering affection for a soothing, but now increasingly outdated, narrative taught to us as school children. Granted its important for children to "enculturate", to be a part of something greater than themselves, to be a part a nation of historical meaning, but such sentimentalities have become tattered nostalgics. The "American Experiment" has run its course, and no longer has relevant continuity with its own past; "America" exceptionalism and self-belief in a providential mission is now a shuttered religion in the land of cynical agnostics.
In a nutshell: the American "experiment" was always rooted in a contiguous American experience - one fueled by ideology (liberty), markets, the westward expansion, and a combination of American identities created "de novo" from that experience: the populist "cross of gold" farmers, the middle-class Babbitt's, the New England bucolic towns, the Appalachian settlement by backwoodsmen, the mountain men, Evangelicals, the feudal south, and the ranchers and cowboys of the far west. To understand WJ Bryan, the cross of gold, and populism you had to understand agrarianism, the grange, and the settlement of the great farming states. To see the civil war, you had to know the institution of slavery and the feudal economic dependency it imposed by the South. To understand isolationism, you could look to the entire history of American views of Europe and the Monroe Doctrine. To appreciate the populating of the West, you had to look to economic opportunity, internal migration, and a vast ranching and farming hopes.
To understand today, however, the American past is increasingly irrelevant. Of what use is it to understand the divisions of the past, which were (with the exception of slavery) almost entirely based on class and regional economic dependencies and today - entirely dependent on immutable racial and ethnic (often imported) and gender animosity?
The commonality found in the American experiment stories and images were rooted not in common experiences - not our differences. Even those who were not WASP saw the "Americanness" and universality in writers and image makers like Norman Rockwell, Mark Twain, O. Henry, Faulkner, T. Williams, E. O'Neill, Willa Cather, Frank Capra, etc. - our painful and unshared experience reserved for the one significant racial minority, blacks.
So what then is left of this experiment? From what historic events is today rooted? All we are, and seemingly will be, are an reinvented alienizing nation with little to share historically (except blacks); 90 million Americans (and growing) mostly of Latin America, India, Asia, and fewer of Islamic origin. All being told that full assimilation is to be rejected, that people of their genetics and coloration are barely a part of the nations experience (or experiment) and that all their grievances are freshly minted and all of one or two generations old.
When a third or half a nation has no historical connection to America, who have no roots as an American invented regional or economic culture - well, what American "experiment" might you be thinking of?
None that I can see.
