Many people think that "political correctness" means "politeness" or "inclusive language" or "avoiding words that hurt people's feelings". It follows that "political correctness gone mad" means "taking that to a crazy extreme, objecting to language that no one has ever objected to"; but that people who complain about "political correctness gone mad" are often rude people who think they should be able to say bad words if they fucking well want to. If Mrs Whitehouse came back to earth and tried to stop the television saying bum and bloody and ding-a-a-ling, the news people would almost certainly accuse her of being politically correct. And also mad, which she very probably was.
However, "political correctness" is also in use to describe a conspiracy theory in which the world is secretly run by a Marxist cabal based in Frankfurt. "Political Correctness" -- and 20th century literary theory, and human rights legislation, and health and safety at work rules, and, very especially and, the idea of man made climate change -- were created by this Marxist clique in order to destroy civilization. What they have in common is that they rationalize unreasonable behavior, and make people do obviously bad things in the name of the greater good. It is obvious that Christian civilization is based upon citizens having cars, refrigerators, and central heating, and air conditioning, so the Marxists have invented the fiction of "global warming" -- which no reasonable person could believe in, and for which there is not a shred of scientific evidence -- in order to make people feel bad about owning these things. PC is an overarching term for the whole plot: believers very often say that it is Political Correctness that says that children have to wear crash helmets to play conkers, or that there is a modern Politically Correct notion that we should reduce carbon emissions. (*)
Obviously, not everyone who has ever used the word "Political Correctness" believes in the conspiracy theory. (I myself have occasionally said things like "some of the older children's books are not very PC"). But believers in the conspiracy theory talk a lot about Political Correctness. And lots of people do believe in the conspiracy. The Daily Mail went so far as to run a headline "How the BBC fell victim to a Marxist plot to destroy civilization". I took this as rather strong evidence that the Daily Mail believed that there was a Marxist plot to destroy western civilization and that the BBC had fallen victim to it, although some people thought that I was reading a bit too much into it.
So. It is possible that when people say that something called "Political Correctness" ("the evil doctrine of Political Correctness" according to Norman Tebbit) was to blame for the Rotheram child abuse scandal, they are talking about "Political Correctness" in the sense of "not saying stuff that hurts other people's feelings, being careful about what words you use". I suppose that what they have in mind is that "you have to be so careful about what language you use about race that it's really hard to talk about race at all; so when there actually is a racial component in some specific crime; it's easier not to talk about it at all and if you can't talk about it, well, obviously, you don't see it."
It is also very possible that Flying Rodent (**) is correct and that after a shocking cock up where serious child abuse was taking place under the police's noses, someone, by way of a damage limitation exercise, said "I know! If we pretend that we can't do anything about dark skinned people molesting little kids because Political Correctness Gone Mad, the papers will swallow it because they love that kind of thing." I can just about believe that PC Copper honestly thought that dark skinned people were free to molest kids if they really wanted to because it was part of their culture and Political Correctness meant that the law couldn't touch them. I don't believe that the entire police hierarchy believed that. (It's also hard to believe that any officer would independently come up with the idea think that "you have to let them rape kids" followed naturally from "you aren't allowed to call them Pakis" unless he had already been told that "Political Correctness" and "Human Rights" were basically the same thing.)
But I think that it is also very likely that when people say that the child abuse scandal was the result of "Political Correctness" they mean that a shadowy group of Marxists was secretly controlling the police, and forcing them to act against "Common Sense" as part of an active plot to bring down Civilization and replace it with a communist superstate. Tebbit definitely thinks that there was a plot to establish an enclave in England that functioned under Pakistani law, as if that followed on naturally from "please use inclusive language".
It seems to me that a lot of these claims -- that Isis or Rotheram or the Girl Guide Oath are "caused" by Political Correctness -- read like nonsense if "Political Correctness" means "the belief that it is nicer to say 'black person' rather than 'n----r'". But they make a kind of sense if you believe that Political Correctness and Common Sense are two dueling ideologies, the one committed to destroying "civilization" and the the other committed to preserving it.
But maybe they are simply nonsense.
(*) I grant that Political Correctness could in those contexts mean simply "Prevailing Orthodoxy."
(**) http://flyingrodent.blogspot.co.uk/2014/09/chicken.html Note that the New York Times essay that Mr Rodent links to is rather more nuanced than he give it credit for