I don't even think liberal Americans believe that. People who advocate for unrelenting immigration would probably be very upset if Russians were coming across the border (or some European, culturally conservative Christian-esque group) by the millions. I would argue those liberals are lying when they talk about what nationhood is. They believe in it, just not the one they live in.
Every now and then you can see glimpses of that. After Muslims went for George W. Bush in 2000, The New Republic of all places wrote an article accusing Grover Norquist of having ties to radical Islam because his wife is Arab: https://newrepublic.com/article/83799/norquist-radical-islam...
If Hispanics and Muslims were coming here and voting their social values instead of their economic ones you can bet the narrative would be different.
