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 as if they’re practically interchangable to build whatever narrative they want, and also to slowly build an association between 'people of ', ‘being a drain on society’, and ‘being here illegally’ to get the average person to side with them.