This has been the American immigrant experience for all but the last 40 years. The major difference is that immigration now just means a few hundred dollars and a few hours out of your schedule. Immigrants are not required to have a stake in American society and culture.
And why are they not? It should be an honor and privilege to come here - or to any of the western civilized nations for that matter. Did the leftists do this to us for votes for multiculturism, divesity? I sure wouldn't move to a country if my heart didn't accept their way of life.
Yes, they are. They are not Americans until they do.