The media’s message appears to have cut through. At the crucial rally against antisemitism in London on Sunday, Zack Polanski, the Jewish leader of the Green party of England and Wales, was not invited to speak, on the grounds that he had not done enough to root out antisemitism from the party. But Nigel Farage was invited, on the grounds that his party, Reform UK, has “expressed very broad support for the fight against antisemitism”. More than two thousand Jews saw things differently and signed a petition arguing that the invitation to Farage “fundamentally undermines” the message of solidarity in defence of Jewish safety and dignity. I agree with them.

Antisemitism must be stamped out everywhere. “Never again” means zero tolerance for this age-old hate, wherever it occurs and whoever voices it. It is indeed a problem on the left, and I’ve often found myself in dispute with those who downplay or minimise it.

Two Green candidates for the council elections have been arrested on suspicion of stirring up racial hatred on social media. The Labour party’s researchers dug up disgraceful remarks by 25 Green candidates for the recent council elections. Never mind that it’s 25 out of 4,500: it’s 25 too many. Polanski’s response when asked about the numerous arson attacks on synagogues and on Hatzola ambulances – “there’s a conversation to be had about whether it’s a perception of unsafety or whether it’s actual unsafety, but neither are acceptable” – seemed dismissive of a horrifying escalation of antisemitic attacks.

So where is the equally urgent concern about antisemitism on the right? It should begin with the media. In the approach to last week’s elections, leading rightwing British newspapers published cartoons of Polanski that many felt could have come from the pages of Der Stürmer, the hate-filled propaganda rag published in Germany from 1923 to 1945.

In the Times and the Telegraph, Polanski was seen as portrayed with a hooked nose (which he does not possess). The Times’s cartoon also gave him the jug ears, receding chin, thick lips and baggy eyes of the Stürmer caricatures, none of which resemble his features. In the Mail, he was shown with an enormous nose, whose shape, again, had been grossly changed.

Worse still was the Sun’s caricature. It turned Polanski into a version of Slimer, a spook from Ghostbusters. It gave the apparition heavy, pitch-black eyebrows, a large bulbous nose, thick lips and a forked tongue, none of which distinguish either Polanski or the original ghost, but all of which figured in Nazi portrayals of Jews. Whether or not this was the cartoonist’s intention, a slimy green monster with red eyes, prehensile fingers and forked tongue ends up coming across as about as crude an antisemitic caricature as you could imagine.

None of these newspapers have issued an apology. The Times’s only acknowledgment of the issue was a column attacking Polanski for complaining about the cartoon. It claimed that “caricature is an accepted part of the cartoonist’s stock in trade”. For sure. But, as cartoonists for liberal newspapers have discovered to their cost, this never excuses antisemitic imagery. Otherwise, its response appears to have been to double down on its attacks against him, charging him with “unwillingness to confront the antisemitism staring him in the face”. In truth, he has moved swiftly to try to root out antisemitism in the Green party, with an accelerated disciplinary process. That seems to be more than can be said for parts of the rightwing press.

The Telegraph has berated Polanski for what it calls his refusal to apologise for that “perception of unsafety” remark. Fine. And shouldn’t the Telegraph also apologise for the way it portrayed him?

The Daily Mail quoted Farage stating: “The Greens will take us to sectarian hell ... No Jew will be safe.” One can only marvel at the sheer brass neck of the man. The Sun has accused Polanski of a “refusal to root out” racists in the party: a “refusal” for which it provided no evidence. So how about rooting out the apparently antisemitic imagery in its own pages?

Where is the storm of protest obliging these newspapers to face their own issues? Where is the Labour dossier on antisemitic comments by Reform candidates? Why does the fury seem mostly to flow in one direction?

I can only imagine what a concerted search would reveal about Reform’s representatives. Comments that have sporadically come to light are just as terrible as the odious remarks of those Green candidates. Far from being rooted out, some of the perpetrators are now elected councillors.

Concerning Farage himself, there are many complaints of claimed antisemitic tendencies (denied by him), beginning at school, where he is alleged to have sung “gas ’em all”, to have given Nazi salutes and to have engaged in antisemitic bullying. Much more recently, he has claimed that “in terms of money and influence”, Jews in the US “are a very powerful lobby”, and repeated classic antisemitic tropes about George Soros and “globalists”, on shows hosted by people viewed by many as virulent antisemites.

To judge by the coverage in the British media, however, you could honestly believe there is unquestionably a bigger antisemitism problem on the left than on the right. The issue is not – and must never be – that the left should get a free pass on antisemitism. The issue is that no one should get a free pass. Yet perversely, the right, the hard right and far right often get away with it.

This reinforces the concern that much of the media might be campaigning against antisemitism not because they care about Jews, but because it’s a highly effective means of attacking – even stopping – the left.

Are charges of antisemitism to be reserved for those who challenge power, or who oppose the genocide in Gaza? If so, this is deeply disturbing. Using antisemitism for political purposes devalues the meaning and urgency of this terrible ideology. It may encourage people to dismiss the latest wave of antisemitic attacks as yet another scare cooked up by the billionaire press. Indeed, this is what I appear to be seeing among some leftwingers who ought to know better.

When the same media produce what look to me like vile antisemitic cartoons, this goes beyond hypocrisy. It seems like a double-edged attack on British Jews, simultaneously instrumentalising and deploying the vicious old tropes. Who on the right will now call them out?

• George Monbiot is a Guardian columnist