According to BBC, there are four significant instances where Jeremy Corbyn is guilty of "anti-semitism".
Most of these items happened years ago.
The 'English irony' video:

in which he said a group of British Zionists had "no sense of English irony".

Former chief rabbi Lord Sacks branded the comments "the most offensive statement" by a politician since Enoch Powell's "Rivers of Blood" speech and accused the Labour leader of being an anti-Semite.

Mr Corbyn said he had used the term "Zionist" in an "accurate political sense and not as a euphemism for Jewish people".

He added: "I am now more careful with how I might use the term 'Zionist' because a once self-identifying political term has been increasingly hijacked by anti-Semites as code for Jews."

The mural row

In March 2018, Mr Corbyn was criticised for sending an apparently supportive message to the creator of an allegedly anti-Semitic mural in 2012.

In a message sent via Facebook, he had appeared to question a decision to remove the artist's controversial work from a wall in east London.

He later said he had not looked at it properly, calling it "deeply disturbing and anti-Semitic".

The artist, called Mear One, denied this, saying the mural was about "class and privilege".

The Holocaust memorial event

Earlier in August 2018, Jeremy Corbyn apologised over an event he hosted as a backbench MP in 2010 where a Holocaust survivor compared Israel to Nazism.

After the Times published details of the event, the Labour leader said he had "on occasion appeared on platforms with people whose views I completely reject" and was sorry for the "concerns and anxiety that this has caused".

And the Tunis wreath row, in which he laid a wreath for the victims of an Israeli bombing in the 1980's.

That's it! This tiny accumulation of years old events is somehow a crisis of racism that absolutely consumes the British press.
As for the Holocaust memorial event, was Corbyn supposed to shout down or throttle the Holocaust survivor?
This "crisis" is all based on conflating Israel with Jews.

Now let's compare this to Israeli Prime Minister Benjamin Netanyahu in just the last year.
Shaking hands with actual Nazis

Oleh Lyashko of the Ukrainian Radical Party came to Jerusalem as part of a parliamentary delegation led by Jewish lawmaker Georgii Logvynskyi. Lyashko was shown shaking Netanyahu’s hand in a video tweeted out by the Prime Minister’s Office.

Lyashko’s party includes nationalist Yuri Shukhevych, the son of Nazi collaborator Roman Shukhevych, whose troops engaged in war crimes against Jews during World War II. Another party lawmaker is Artyom Vitko, who was filmed in 2015 singing a song celebrating Adolf Hitler with lyrics that included “Adolf Hitler, together with us, Adolf Hitler, in each of us, and an eagle with iron wings will help us at the right time.”
...
In an interview with The Times of Israel published Tuesday, the prominent American Holocaust historian Deborah Lipstadt called Netanyahu a hypocrite, saying that “you have a government whose policy is to make nice with the Polish government, which is trying to rewrite Holocaust history, and with a Hungarian government that’s engaging in anti-Semitism.”

Call me provincial, but being buddy-buddy with nazis that sing songs about Hitler is generally a sign of a anti-semitism. Can you imagine the reaction of the media if Corbyn had shaken his hand?

There is also the rumors that Israel is sending weapons to Ukrainian neoNazis.

Netanyahu has also met with Hungary’s Prime Minister Viktor Orban in 2017, a man who has been accused of anti-Semitism.

Then there are the things that Netanyahu are silent on.
For instance, he was silent for three days after a neoNazi car attack killed Heather Heyer.
Netanyahu also doesn't have anything to say about Germany’s Alternative for Germany (AfD), a far-right party who has roots in Germany’s Nazi legacy.

Basically, if someone was to use consistent and honest standards, Netanyahu is obviously the anti-semite, not Corbyn.
And do you know who knows this to be true? American Jews.

“Go home,” Simon wrote in a caustic message to Naftali Bennett, an ally of Prime Minister Benjamin Netanyahu who serves as Israel’s minister for the diaspora. “Netanyahu’s interventions in US politics aided in the election of Donald Trump and his raw and relentless validation of white nationalism and fascism,” Simon wrote. “The American Jewish community is now bleeding at the hands of the Israeli prime minister. And many of us know it.”

Simon was not alone in his criticism of Bennett’s visit. “NO THANK YOU,” Rebecca Vilkomerson, the executive director of Jewish Voice for Peace in New York, replied to Bennett’s tweet about his visit. “Your racist worldview has more in common with the perpetrator of this attack,” she told Bennett, who supports Jewish-only settlements in the Israeli occupied West Bank and the expulsion of African asylum seekers from Israel.

The Pittsburgh chapter of If Not Now, a group of young American Jews opposed to their community’s support for the Netanyahu government’s nationalist policies — including the building of a wall along Israel’s southern border to block African asylum-seekers — protested Bennett’s visit at a vigil on Sunday near the Tree of Life synagogue, where the shooting took place. “The inspiration for this attack,” If Not Now member Ren Finkel said, “is the anti-Semitic rhetoric of Trump and other Republican leaders.”
...After Trump’s election, Netanyahu also refused to condemn the president’s repeated incitement against Soros, Simon noted, even as the president and his Republican allies fed their followers “a steady stream of conspiratorist horseshit so acutely racist and anti-Semitic that the name of a Holocaust survivor can now be invoked as a fixed dog-whistle for Jewish conspiracies against white nationalist America.”

The Pittsburgh gunman cited as justification for his massacre of Jews a baseless conspiracy theory about Soros, which has been promoted by Trump’s favorite cable news network, Fox News, and Rep. Matt Gaetz, a Florida Republican endorsed by Trump — the false claim that, as Simon put it, “a Jewish financier is paying brown-skinned people to journey to our southern border and menace our nation.”

The smear of Corbyn reminds me of Kerry's swiftboating in 2004.