The New York Times apologised this week for a cartoon published recently in its international edition. The drawing was of a blind Donald Trump, wearing a skullcap, led by the Israeli prime minister Benjamin Netanyahu, who was depicted as a dog wearing a star of David collar. The cartoon evoked caricatures of evil Jews misleading blind nations, of a kind popular in the German media during the Nazi era.

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The reaction in both the US and Israel was first shock, then a furore. The cartoon couldn’t have come at a worse time – the San Diego synagogue shooting last weekend proved that antisemitism is still deeply rooted in the US. And it came just as Israel prepared to remember 6 million Jews on the national Holocaust Remembrance Day. For New York Times columnist Bret Stephens, the cartoon “checked so many antisemitic boxes that the only thing missing was a dollar sign”. The Jew in the form of a dog; the small cunning Jew leading a naive American; hated Trump depicted as blind and Judaised, a puppet of the Jewish state (as if Trump needs Netanyahu to make him act the way he does).

I found it shocking – even more so when my five-year-old spotted my computer screen and asked “what is the dog doing?”. We haven’t discussed the Holocaust with my daughter yet. We’re still figuring out how to let her know that half of her dad’s family is dead because of antisemitism. Living in a Jewish state, celebrating all the holidays and Shabat since she was born, I’m not sure she yet knows that she is Jewish or even what a Jew is. I certainly don’t want her indoctrinated into Netanyahu’s narrative – that the whole world hates Israelis because we’re Jews.

But depictions such as the New York Times one and the ongoing antisemitism blindspot in the British Labour party make me wonder. They give the Israeli right a loaded gun – confirming its basic assumption that any criticism of Israeli government policy is driven by hidden antisemitism.

Netanyahu’s rightwing government seeks constantly to convince the Israeli public of this narrative. The Israeli left, by contrast, constantly struggles to prove that it is valid to criticise Israel, and that those of us who oppose the Israeli government’s policies are not “self-hating Jews”. In this context, an antisemitic political cartoon actually empowers the right.

Holocaust Remembrance Day has always been a battlefield between Israel’s left and right. While the left insists that there is a universal lesson to be learned from the Holocaust, about the dangers of nationalism and racism, the right argues that Israel should instead learn to be the toughest bully in the neighbourhood. While I also see the Holocaust as the ultimate proof of the need for an Israeli state, I’m repulsed by the way the right uses antisemitism to justify Israeli occupation of Palestinian territory. “We were persecuted across the world,” they say, ”now the world owes us our own big state.” But as the late novelist and peace campaigner Amos Oz wrote: “Israel is a refugee camp, Palestine too. The conflict is a tragic clash between the right and the right … both nations don’t have another place to go. They cannot unite into a big happy family, because they are not family, and they are not happy – these are two miserable, different families. A historical compromise must be made: a two-state solution.”

Many in Israel called Oz a traitor. For me he was the ultimate Zionist. A Zionist who criticised the Israeli state, not from a desire to destroy it – but out of concern for the future of Israeli democracy. Those in the international left who question the existence of the Israeli state are damaging the Israeli-Palestinian struggle for peace. How can we persuade the Israeli public to take a leap of faith and negotiate an agreement, when you call for the termination not just of the occupation, but the entire country?

While I trust a figure such as Oz to criticise Israeli policy without being antisemitic, I do wonder about some members of the UK Labour party and the New York Times cartoonist. There is a lesson about self-awareness here. People might believe they are impeccably liberal, but it’s still worthwhile to keep checking one’s intellectual reflexes. For example when you began reading this piece, did a small part of you think: “Here are the Jews again whining about antisemitism”?

If the international community wants to be involved in the solution of the Israeli-Palestinian conflict, it must abolish all traces of antisemitism. Otherwise, we cannot march together.

• Ayelet Gundar-Goshen is an author and psychologist. Her new novel is Liar