Not everyone thinks this, but I know an extreme right-winger who thinks this. He is also a conspiracy theorist who thinks non-white people are out to get white people so, yeah, odd.
Not every immigrant is illegal or bad. I know a girl who didn’t speak English for 3 years when her family legally immigrated, so of course she’s been told this.
It’s origins (and current day continuation) are in white nativism which of course intersects with the white supremacist and American exceptionalism sentiments that has been around since the origins of the US