GERALD Scarfe and Steve Bell, two men who colour in drawings for the London papers, have been causing offence.

This, as any decent cartoonist will tell you, is easy to accomplish. Funny pictures bother some people far more than any number of words. This is strange, but true.

Last weekend, the Sunday Times published a drawing by Scarfe showing Benjamin Netanyahu, Israel's prime minister, building a wall with blood-red cement. Between the bricks, crushed in agony, were Palestinians. Above them, Netanyahu glowered, sword-like trowel in hand.

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On Wednesday, the Guardian's website ran Bell's regular op-ed comment cartoon, this time on the wording of the independence referendum. "Do You Agree That Scotland Should Go And ... Itself?" ran the lettering. The missing word was blotted out by a potato-headed caricature of a cross-eyed Alex Salmond in Saltire face-paint.

The two cases were not equivalent, of course. No-one is about to die for Scottish independence. Reactions to the satires were strangely similar, for all that.

Hardly had Scarfe's work appeared than he had the Anti-Defamation League, the Board of Deputies of British Jews, and the Israeli ambassador levelling accusations of anti-semitism. Scarcely was Bell's art on the web than hundreds of comments had appeared. Many of those from Nationalist Scots – there were others – denounced the cartoon as racist.

At the Guardian, as elsewhere in civilisation, there is no worse charge. Poor Bell – no relation; none whatever; his loss and so forth – has been ploughing a lonely furrow since the last election, when his forward-thinking paper advised readers to vote Liberal Democrat in the "progressive" cause. Who couldn't be a maverick in such a circumstance? Being funny is trickier.

The missing part of his drawing was one of those F words, but I don't think "free" is the one we're looking for. It doesn't seem likely, either, given the droll image of Salmond, that a sentiment was being put into Unionist mouths. No: doesn't work. Perhaps disgruntled at the prospect of reliable Jocks withdrawing from the anti-Tory fray, Bell seemed to be telling Scotland, straightforwardly, to go and f*** itself. Fair enough.

Scarfe was meanwhile at the heart of a proper international mini-incident. His ultimate boss, Rupert Murdoch, disowned him in one of those new-fangled tweets. His temporary editor, Martin Ivens, apologised and said, with a certain unconscious wit, that the artist Scarfe had "crossed a line". By employing red ink he had, apparently, revived the ancient blood libel against Jews. And he had done it on Holocaust Memorial Day.

That, for my money, was a mistake, albeit Scarfe's only mistake. A comment on Israel's attacks on Gaza, on its treatment of Palestinians generally, on its wall-building and its illegal settlements, would have kept for another week and averted the spurious charge of anti-semitism. The chance to be mortally offended, useful so often to right-wing Israeli politicians, would have been denied. Wouldn't it?

You can never be sure. Writing about the Scarfe cartoon (in the Guardian, ironically) Mark Gardner of the Community Security Trust, a charity dedicated to the protection of British Jews and to monitoring anti-semitism, made a remarkable claim. Describing the blood libel – the slanderous fantasy that Jews have used Gentile blood in "rituals" – he said: "The actual intentions of Gerald Scarfe and the Sunday Times count for very little within this broader context of history, and its contemporary emotional and racist impacts."

Gardner went on: "So, the cartoon, regardless of the wishes of Scarfe and the Sunday Times, regardless of it specifically being anti-Netanyahu rather than anti-Jew, will seriously distress many Jews and will give pleasure to many anti-semites."

So here we are in the land of offence. It doesn't matter what you mean or intend. Context is irrelevant. Facts that might explain a comment or its motives can be disregarded if the offended demonstrate even the possibility of moral collateral damage. Yet Murdoch and his editor – perhaps we should expect no better – couldn't wait to apologise for Scarfe. He broke no law, but he was deemed guilty all the same. When you are next "outraged" by something, bear in mind what's at stake.

In another piece of irony, Bell has been in the same position as Scarfe in relation to Israel, and faced with the same sort of allegations. Last November, he too produced a cartoon of Netanyahu under a "Vote Likud" banner, surrounded by missiles, with William Hague and Tony Blair as a pair of glove puppets. Mark Gardner (the same) said Bell was employing "the anti-semitic trope of Jews as puppeteers, controlling the politicians of ostensibly much more powerful nations".

The cartoonist denied the charge fiercely. He had been after a "specific politician" and certainly not all Jews. Yet in last week's referendum cartoon, a minor matter to be sure, the caricature was of Salmond but the sentiment offered was to "Scotland". That's pretty inclusive. Does it matter? Or rather, does the right to offer a tainted comment still matter more than the offence caused?

One weird consequence of the digital age is that human skin seems to grow thinner by the month. You can almost predict the arguments, issues, even words, that will set off the emails and the twitterstorms. Certain commentators think this is a new, fun part of the game, there to be manipulated. The rest of us wonder where it might lead. So-called digital democracy is even easier to rig than the mundane variety.

The potency of cartoons in this new world is odd. Millions of words, some hostile or plain nasty, had been written about Islam before Denmark's Jyllands-Posten paper set off the "Muhammad cartoons controversy" in 2005. That didn't matter when a few drawings caused riots and worse around the world. It counted for something, though, when self-censorship became evident in the Western press. Someone – or something – had won.

Last April, back among the banal, The Economist newspaper-magazine printed a map of Scotland on its cover and decided to rename the country to demonstrate "the price of Scottish independence". With humour so heavy you couldn't have lifted it with a crane, we became Skintland, land of Glasgone, Donedee, Edinborrow, the Grumpians and the Highinterestlands.

Aside from the fact that it wasn't funny – clearly, Woody Allen was busy – it should have been laughed off. But there was Salmond, insisting: "It just insults every single community in Scotland" – they take The Economist? – and proclaiming: "This is Unionism boiled down to its essence." Talk about falling for it.

In fact, it was propaganda done badly. In the ensuing fuss the telling fact was that every affronted child of old Scotia went on about the heinous cover and forgot to mention the (entirely disputable) words inside. Such is the problem with offence: it supplants argument. And that fact can cut in either direction.

Scarfe allowed Israel and its supporters to evade all discussion of Netanyahu's despicable behaviour. Bell simply confirmed Nationalists in their belief that London's press is biased and ignorant. Neither artist deserves to be pilloried for it. Scarfe's critics should look at the truly anti-semitic stuff floating around the Arab world. Anyone in the huff with Bell should acquire a sense both of humour and perspective.

I could invite the Guardian's man to go and - himself in return. But I'm keen on a Yes vote. I therefore conclude that he's just done me a favour. Now, that is funny.