I thought of another way to express my point in terms of your post:
>>American culture is uniquely predisposed to liberty
The problem is our culture has changed in this aspect (and others) - and not due to immigrants. Even without immigration our culture remains the same, resulting in the same problem.
What makes you think it isn't due to immigrants? California has gone deep blue thanks to immigration. This alone creates a massive electoral college disadvantage for conservatives. No mass immigration and California might still be electing Ronald Reagans.
Issue by issue the pre-1965 population and their children and grandchildren are less well disposed towards big government than the immigrants and their children. This holds true even for economically successful groups. Looking at the scope of history there has been very little liberty anywhere at any time.
It should be no surprise that people from cultures with no history of liberty, where authoritarianism is the basic philosophy (as is the case in the muslim world), will carry their disdain for freedom with them.