America isn't everywhere, it is a real place and Americans are a distinct people and culture.
Yes, but it's an evolving, assimilationist people and culture. It used to be a British Protestant people & culture (not "Judeo-Christian" as modern conservatives like to imagine). Some Founders refered to themselves, even after the Revolution, as "Englishmen."
I know you've heard this before, but ...
Catholics, Germans, and Irish were deemed non-American in the 1840s. Jews, Italians, and East Europeans were deemed non-Americans in 1900. But they assimilated.
There's no reason -- none -- that Mexicans, Arabs, and Muslims can't assimilate into America over the coming decades.
If we can go from being a Protestant nation, to a Christian nation, to a Judeo-Christian nation, there's no reason we can't become a Judeo-Christian-Islamic nation. It can happen. It likely will happen. And I have no problem with that. None.