How anybody can draw a connection between expressing the opinion that it's better not to use certain terms, and censorship, is beyond me. Censorship is only an issue when a government is exercising coercion. To express the opinion that use of a term is inappropriate, and to persuade private businesses of journalism and broadcasting to exclude certain terms from usage in their own media voluntarily, has nothing whatever to do with censorship. Moreover, the use of the phrase "the PC Nazis" is appalling to me. To compare a person who expresses the opinion that people should use language in a considerate manner with mass murderers makes no sense. I think people who use the term "Nazi" to refer to everything they disagree with is disregarding the real evil that Naziism was and is.
What's more, there have always been norms of etiquette and appropriateness of terms. All that changes is what the actual norms are. Now, if people were in danger of being arrested and jailed for use of offending terms, it would make sense to me to say we had a problem. I'm the first to believe in freedom of speech. But freedom of speech does not, and can never, mean freedom from being criticized for one's speech.
I have come to the conclusion that the definition of political correctness, for some people, is any suggestion that we should behave like decent human beings in our use of language and custom. Political correctness happens to be at the top of my list of terms I think we'd be better off without. And I happen to agree that "illegitimate child" is a bad term. I won't favor having you arrested for using it, but I certainly may regard you as a less-than-considerate person for it.