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.
Short answer is “propaganda”. News agencies against immigration will pretty regularly swap between “illegal immigrants”, “immigrants”, and <insert current target race here> as if they’re practically interchangable to build whatever narrative they want, and also to slowly build an association between ‘people of <insert race>’, ‘being a drain on society’, and ‘being here illegally’ to get the average person to side with them.