Another way in which Political Correctness differs from 'treating other people with respect'. The principle of respectfulness is amenable to reason, and people arguing in good faith can arrive at a rational consensus about treating each other respectfully.
But Political Correctness enforces an irrational 'heads I win, tails you lose' relationship: Either you mouth the shibboleths of the in-group, or the in-group rejects you. There is no appeal. There is no room for people of good faith to disagree. There is no allowance for people to reach a mutual understanding in spite of their initial differences in terminology and outlook.
If somebody refuses to discuss the issue of immigration with you, because they object to your use of the term 'illegal immigrant', that is not respect, that is political correctness.