IMO, people who complain about political correctness usually strawman their opponents with the "herstory of womyn" type argument, which really doesn't represent anything but a small minority of political correctness advocates.
Really though, what political correctness is really about is respect. Complaining about, say, referring to a trans* person with the pronoun of the gender they identify with instead of the pronoun of their biological sex is disrespectful and impolite. Team names like the Washington Red****s are disrespectful and impolite. Using the term "illegal" instead of undocumented immigrant is disrespectful and impolite. There is, of course, a sliding scale of rudeness (with the first two being more offensive than the 3rd) but all of them are about respecting different people.
How is that disrespectful and impolite? I mean, they immigrated illegally, so that's the most logical thing to call them. I can understand the first two, this one is just seems ridiculous and oversensitive.
Lets call them what they are. If you avoid paying your taxes using a hidden bank account, you are committing a crime. You become a tax cheat. If you steal, you are committing a crime. You become a thief.
So when you immigrate to a country without registering with its government, you are committing a crime. Illegal immigrants are illegal. They are common criminals by nature of their existence as long as they are on American soil until the register with the government.