America works as a multicultural society, to the degree that it works, because it has a unifying secular religion ("Freedom and Democracy") that is undergirded by a pervasive religious culture, mostly Christian, heavily evangelical.
Break down that unifying ideology, and the country will come apart at the seams within a generation.
If you only know America from Hollywood or CNN, you will miss the America that works, I suppose the kind of people who wind up in Hollywood or CNN are a self-selected group that hardly knows their own country. This secular religion rooted in evangelical Christianity is able to absorb the most diverse streams of immigrants, and tie them all together into a fairly raucous, fairly chaotic, but ultimately functioning unit.
It has to be noted that during most of our history, the greatest number of immigrants came out of various Christian cultures, whether they were themselves as individuals believers or not, and aside from a few bumps in the first generation, absorbing them has not been that difficult.
The greatest disaster to befall us has been the capture of our schools and universities by the Left, which is openly hostile to the very thing that holds us together, and has systematically eliminated any reference to it from public education at any level. The unifying ideology that was once inculcated consciously in public education is no longer taught, it has to be absorbed from your family or out of the air, if at all. This is disastrous in a "multicultural" nation of immigrants.
Eliminate the "under God" and the country will fall apart, and no one will miss us. Its never been necessary that everyone believe in the secular religion, and it certainly has never been necessary for everyone to be a Christian believer, but it has worked to the degree that it worked because there was a critical mass of believers who provided the common philosophical language which was and is the glue.
Most countries are ethnic entities, and it doesn't matter what you believe, you are still French, or German, or whatever. We are not, we are a uniquely ideological entity which is our strength and our weakness. We can absorb immigrants in numbers that would overwhelm any other country, and come up laughing. But even we can be overwhelmed, if first of all the numbers are too great for assimilation, or even worse if having stripped the public space of any reference to our unifying national religion there is nothing to assimilate to.
France is also ideological - you can be French no matter what is your religion or race. And French were the example for Americans.