The Corbyn-supporting Momentum movement was this week accused by some Labour MPs of downplaying antisemitism. Then it got worse, as Jackie Walker, the group’s vice-chair – already suspended from the party once over antisemitism – made cringe-inducingly unpleasant criticisms of Holocaust Memorial Day and more. Rightly, she now faces calls to resign.

Not for the first time, the wider suggestion is that the party has a wide-scale problem. And not for the first time, it feels as though British Jews have become a political football in the bigger battle over the party’s leadership.

Antisemitism is manifestly real and exists within the Labour party, as it does within British society. The surge of new members – the party now has more than half a million – will no doubt reflect that. In recent years, the climate in the UK has palpably worsened – to a great extent, dismayingly, because of the Israeli-Palestinian conflict. Witness the spikes in antisemitism that cluster around Israel’s Gaza invasions.

But there is no evidence that Labour is now overrun by antisemites. And the problem with tying antisemitism to Labour’s current leadership is that it corrodes the capacity to talk sensibly about the subject. While many accusations come wrapped in anti-Corbyn sentiment, some of his supporters – so routinely vilified and besieged – dismiss the claims outright. The ensuing back-and-forth is increasingly painful to watch.

Jeremy Corbyn has repeatedly stood against antisemitism. Labour’s leader emphasised this again in his conference speech and at the Labour Friends of Israel fringe event, where it was noted that there had been real progress. Party members recently suspended over antisemitic comments have been swiftly dealt with. In fact, most had made those comments before Corbyn came to power. He set up the Chakrabarti inquiry precisely to stamp out this prejudice. And even if you doubt Corbyn, there’s no doubt that the ensuing report contains solid, usable recommendations, along the lines made by groups long engaged in tackling antisemitism.

Jeremy Corbyn and Shami Chakrabarti: ‘Her recommendation that Labour implement training on antisemitism is welcome.’ Photograph: Jonathan Brady/PA

Still Corbyn, his supporters and progressives in general are not inoculated against being antisemitic or racist – or sexist, for that matter. Progressives for whom the Palestinian cause is important can have blind spots over, and be desensitised to, antisemitism. Yes, it’s hard to admit susceptibility to such “isms”, but acceptance (we are all susceptible) really is the first step. And the onus is on the progressive left to get this right (this step being one of the things that “progressive” means). So it doesn’t work for the left to counter accusations of antisemitism by saying the Tories have a bigger racism problem: true, but hardly the point.

Neither is it helpful to point out that supporters of an expansionist Israel use claims of antisemitism to shut down debate. Again, true: but so what? Are you seriously suggesting that all complaints of antisemitism are crying wolf?

The Israeli-Palestinian conflict has long been a core issue for the Labour party, and a leader who is more openly critical of Israel than his predecessors may well lose support among those backing a very rightist Israel. But at the same time, exasperatingly, discussions around Israel, Palestinians and the British Jewish community can drive a wedge between progressives who might otherwise be united over common causes: raise the issue of antisemitism and you may be dismissed, or told that criticism of Israel is not the same as antisemitism. A true progressive would give careful consideration to suggestions that their language or views are offensive and alienating. The Israeli-Palestinian conflict does not make antisemitism an exception to the rule.

People with shared aims and causes build a strong, unified political force by staying in conversation with each other. That means challenging antisemitism, rather than overlooking it, downplaying it, or walking away.

'Her report focuses on the way Israel is discussed: stop saying the manifestly racist 'Zio', and leave Nazis out of it'

None of which is to absolve abhorrent views – but the idea is to encourage more responses like those of Naz Shah: suspended over antisemitic comments, the Labour MP for Bradford West apologised and then, with support from the local Jewish community, developed her understanding of the issue.

In similar vein, Shami Chakrabarti’s recommendation that Labour implement training on antisemitism is welcome. Her report focuses on the way Israel is discussed – stop saying the manifestly racist “Zio”, use “Zionist” only advisedly, and leave the Nazis out of it. Underlying much of the hostile language seems an inability to comprehend that Jewish people can hold power (in Israel) and be victims of antisemitism (everywhere), all at the same time. And let’s be honest: for some, antisemitism pales when set against the plight of the Palestinian people (as though we should rank such things, rather than tackle both).

Dealing with this deep-rooted and so often denied hatred is continuous and often infuriating. But if we engage with it honestly, in all its complications and outside of Labour’s internal power struggles, the progressive left can genuinely take on antisemitism – effectively and together.