Is it possible to crack a joke these days without offending someone?

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Have we all become so "precious" that we can't make an innocent humorous remark without causing offence? The TV football pundit Gary Lineker, when introducing last week's Match of the Day on BBC TV, said "It’s a strong start to the premier league season. Real hair-raising stuff at times… unless you’re Alan Shearer and Danny Murphy." The reference was to his two fellow pundits, sitting opposite him, who are both almost completely bald. They both appreciated the joke, but poor old Gary has had a real roasting from some members of the public for his apparent bad taste in poking fun at bald people. This follows an incident last week when the result was announced for the best joke from a stand-up comedian at the Edinburgh Fringe. This was from a Swedish comic who said "I keep shouting 'broccoli' and 'cauliflower' - I must be suffering from florets". This was roundly condemned as poking fun at sufferers from Tourette's Syndrome. What do you think? I would agree that jokes that are racist or sexist should be avoided - apart from anything else they are rarely funny for that very reason - but haven't the two examples I have quoted taken this attitude a bit too far? By the way, I personally reckoned that another Fringe joke should have won: "I'm going for an Eton-style Advent calendar this year - all the doors will be opened by my father's contacts". Or is that too much of an insult to Old Etonians to be permissible?