Of course, but work colleagues / friends and other people can always over hear things which were not meant for them to hear. People will choose to be offended, sometimes on behalf of others - which is even worse.
There are ways to behave in public, but then there are people who also stick their nose in other people's business which is not helpful.
I think we're in agreement and talking at cross purposes here, most people know how to behave in front of others (those with a modicum of social skills at any rate). However, if someone slips up, they shouldn't be demonised for it or people shouldn't be out for blood just because of an innocent mistake.
Even for the nursery rhyme - as I said, even I was taught it as a child (a long time ago) it was a generational thing, and it was just a rhyme that existed - of course it is wrong to continue it, but when it's embedded into you, like tying a shoelace it is hard to unlearn. Does it make him racist for doing it? No of course not - it makes him a bit daft not to be more careful about what he is saying in front of the camera, but then again it could have been handled/edited better, and you know what? He stopped himself from saying it. In fact the majority of the black population responded that they saw no offence in the comment and it was out of context anyway.
My parents generation talk about "coloured" people - they didn't know any better until they're told they can't say it any more. There are a plethora of terms and things that have changed so much and so quickly over the past generation that people will slip up and this is important WITH NO INTENT to offend. Heck, even the Golliwog symbol on Roberstons jam was a big fracas (

) over nothing.
I suggest that if you find that sort of stuff unacceptable you never go to a comedy show! Comedians are not decent people by your definition!!