Perhaps the best thing would be to say "illegal immigrants"
The majority of legal immigrants know the struggle to become citizens, but also don't want to feel like they wasted time because of what's happening currently.
"You want to come to the United States? Go for it, just do it by the book"
There is no such thing as an "illegal immigrant" in this country. It is not illegal to be in the US without papers, no matter if you entered legally or not. And "entering legally" means going through a checkpoint. You have to do that regardless of whether you're a citizen or not. Plenty of undocumented immigrants enter legally and then overstay their visa, which is not a crime in the US. It's literally not part of the criminal code.