A culture with a less than 2.1 fertility rate is doomed to extinction?

That would certainly be news to the Chinese!

Their culture is flourishing and their economy booming and the gov't has been trying for years to enforce a fertility rate of 1.0!

Perhaps the greatest wrong assumption here though is that the culture of immigrants is static and unchanging from the land of their birth. It's not. People change and adapt, and assimilate (even if they don't learn the languange, amazingly) when they move into a new land and a new host culture. A Latino or Muslim who's lived in America for a generation is dramatically different in culture and identity from a Latino or Muslim who just crossed the border. However, to the kind of ugly racists who make these kind of scare videos, we're all one big, threatening, unchanging, monolithic alien blob.