It can get worse (and it did).
Imagine you are an employer and want to fill a vacant post. More candidates have appeared and from them you considered one to be the best. Unfortunately it is a white heterosexual man who does not publicly express his religion and political opinions. You ...! If any of the others is a woman or a member of any ethnical, religious or sexual minority (or just has different political opinion than you), you are not allowed to hire your favorite candidate. At least if you want to avoid public dehonestation, racism or sexism accusation etc.
Unfortunately, when it seemed that open racism has finally disappeared, the PC policy is starting to build a new wave. It is similar to eco-politics or EU-socialism which start to resemble 1984. Orwell was right, just missed it for about two decades. If you have a different opinion, you commited a thougt-crime and deserve to be strongly accused and dehonested. This is what is wrong, it's just another form of totalitarianism which doesn't help anyone and just makes life more difficult for the disadvantaged whom it was supposed to help.
Anyway, it was an old nursery rhyme. Jeremy should have done without it, it was stupid, the word is horrible, but it wasn't aired, it was an intentionally leaked outtake and from this point it should have been viewed. He should say "sorry", take care not co cock-up again, BBC might have given him a fine, but that should have been all. Not that huge affair.