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.
Remember, everyone is a hypocrite. The USA is a melting pot of so many different peoples with about 250 years of history as a nation. My working theory is that has led to a nation-wide identity crisis: who and what am I. They are intensely occupied with their origins because the only people who have been on the continent for millennia (Native Americans) were brutally reduced and are the only ones who know their roots with higher certainty.
It’s why many USAians will gladly call themselves “Italian”, “Indonesian”, or “African” without ever having set a foot in that country/continent, knowing next to nothing about it, being unable to speak or even identity a language from there, nor locate it on the map.
Factor in their education system, “winner takes all” vote counting system which leads to tribalism, and media influence, human inability to think long term, and you end up with a large swathe of people who cannot reason logically about these things.
They are both from those countries and completely USA people. Bit baffling really.