If we ignore the "it's all an evil Tory conspiracy run by Murdoch" line, there are two narratives around the current problems the Labour Party faces with anti-semitism. One is that the Party isn't fundamentally anti-semitic but has a few members who have spoken or written things that constitute anti-semitism. The other is that the Party has a fundamental problem, to coin a phrase, it is institionally anti-semitic.
Chris Dillow makes the case for the first narrative:
It might be useful to distinguish between two forms of racism: verbal, and structural. Although the two often go together, they need not. For example, you’ll hear far more racist language in financial firms than in the arts industry – but you’ll also see far more ethnic minorities too. One business has more verbal racism, the other more structural racism. In this sense, Labour has a problem with verbal racism, but isn’t obviously structurally racist.
Now taken in the round, Chris is quite right here. Even its biggest critics (and I count myself as one of these) wouldn't see the Labour Party as structurally racist, indeed the Party can make a strong claim to having been instrumental in making Britain a far less racist country than it was when I was growing up. On the specific question of anti-semitism, however, I fear Chris might be wrong - the faction that has captured the Party right now, the Corbyn-Abbott-Livingstone axis does have a structural problem with anti-semitism. And at the root of this is the left's (if it's OK to describe Corbyn's faction in such terms) attitude to Israel.
It's not simply the left's 'edginess' (as Chris calls it) that's the issue here but that the adoption of unquestioning support for Palestinian rights had led them into sharing campaigns with mysogynist, homophobic and Jew-hating groups simply because those groups are opposed to Israel. And, as Jonathan Fredland observed in his plea for the left to treat Jews as they would any other minority, 93% of Jews see Israel as part of their Jewish identity. The support of Corbyn, Abbott, Livingstone and others for organisations that present an existential threat to Israel, that literally wish to destroy the world's only majority Jewish country, isn't seen as 'anti-Zionism' but as an attack on Jews and the idea of Jewishness.
The result of this is that too many from the left are simply blind to how their words and actions around Israel are deeply upsetting to many Jewish people. When Livingstone said Hitler supported Zionism what Jews heard was that the man who sought to exterminate all Jews and killed over 6 million, far from being an anti-semite was a supporter of a Jewish homeland. Livingstone and those who act as apologists for his racism in effect declared that Zionism and National Socialism had the same ends. That so many in the Labour Party fail to realise that this view is horribly anti-semitic says to me that this isn't just 'verbal racism' - the left is institutionally anti-semitic for the same reasons that the the Lawrence Enquiry found that London's police were institutionally racist.
I'll conclude by saying that, while Chris Dillow is correct about the persistence of dog-whistle politics and right that it should be challenged - the attacks on Sadiq Khan in London are appalling - this is essentially 'whataboutery'. What the left needs is to recognise is that it doesn't treat Jews in the way it treats other minorities - in the game of equalities top trumps, anti-semitism is bottom of the pile.