What is Labour’s anti-Semitism row really about? The party’s warring tribes can agree on the battlefield – adopting the full definition of anti-Semitism from the International Holocaust Remembrance Alliance (IHRA) – but they can’t even unify on what’s at stake, let alone what the resolution should be.

For Jeremy Corbyn, the battle is about foreign policy. He believes that the IHRA definition – which Labour has included in its code of conduct in a modified form – could restrict criticism of Israel. That view is shared by some in his office and inner circle, including his strategy chief Seumas Milne. Yet the reality is that the most influential foreign policy strategist in the leader’s office is not Milne – or former NUT organiser Jennifer Larbie, the nominal head of foreign policy – but Corbyn himself.

Among otherwise loyal pro-Corbyn factions, there is another view. They fundamentally see adopting the IHRA definition as reassuring British Jews of the party’s good intentions and burying the row to avoid it becoming the story of the summer. Those who hold this opinion include many MPs, staffers in the leaders’ office, senior members of the grass-roots organisation Momentum, and the prominent commentators and pro-Corbyn members of the party’s ruling National Executive Committee (NEC) who liaise with the leader’s office via a WhatsApp group.

Some share Corbyn’s concerns about the possible abuse of the definition. However, they know that any ambiguities in the text – which was not written with the intention of being used to underpin regulation – can be ironed out by the NEC, on which the Labour left has a comfortable majority. So they regard it as a risk worth taking.

Who is right? After its dramatic realignment, Jeremy Corbyn’s Labour now resembles a newly minted state: it has a democratic constitution but not a democratic culture. As one former party staffer – long departed from a job overseeing the Labour constitution – told me recently, their job was essentially to “find ways to use the rule book to fuck people”. The exact rules matter less than who gets to interpret them.

The ambiguities of the IHRA definition mean that a Labour Party with a different leader, NEC and general secretary could use it to remove Jeremy Corbyn and his allies, by demonstrating that their criticism of Israel as a racist state went beyond what is allowed. But the truth is that when Corbyn steps down, he will do so voluntarily and almost certainly to a successor who shares his politics. And if some shock event leads to a revival of the party’s Corbynsceptics, then their first order of business will be implementing the full definition in any case. So the current situation is irrelevant.

It’s not uncommon for disgruntled Corbynsceptics to describe his hegemony as a “nightmare”, yet his allies still behave as if his grip on power were fragile. The truth is that Corbyn’s hold on the Labour Party’s rule-making institutions is secure and his priority should now be using that hegemony to win the next election.

One person who is well aware of Corbyn’s dominance within the party is his chief of staff, Karie Murphy. She is the most influential member of a third faction, which is, again, well represented in the leader’s office and among the project’s outer circle. Murphy sees some of the complaints about anti-Semitism as a vehicle for challenging Corbyn’s authority. That is why she argued against others in the inner circle, including Momentum’s Jon Lansman, who called for an end to the disciplinary charges against Labour MPs Margaret Hodge and Ian Austin. Hodge had called Corbyn an “anti-Semite and racist”, while Austin confronted the party chair, Ian Lavery, about the issue in a hotly disputed row. (Some say that Austin shouted and swore; others, including Austin himself, deny this happened.)

Hodge faced immediate disciplinary action over her remarks, while the party machine has been notably slower to act against ordinary members accused of anti-Semitic behaviour. Other senior Corbynites argued with Murphy, saying that the double standard made the party look bad. Their fear was heightened by Hodge’s decision to ask Mishcon de Reya to act for her. The London law firm specialises in discrimination cases, while Labour’s lawyers are more at home in cases involving electoral law, data protection and human resources.

In the end, the leader’s office stepped back from the brink, dropping the proceedings against Hodge. (The case against Austin is still unresolved.) This is significant: at least 12 Labour MPs were prepared to resign the whip if the veteran MP for Barking, east London, had faced further action.

But the deeper problems are yet to be settled. Some of Corbyn’s opponents agree with the “Lansman view” – that the party should now reassure British Jews and move back to economic policy, on which Labour is largely united. Others agree with Corbyn that this is a foreign policy issue but draw a different conclusion: his views on Israel and the West generally make him unsuitable to be Labour leader, and prime minister.

Austin is one of this group. The MP for Dudley North has declared that he regards Corbyn as outside Labour’s traditions and unfit to lead the party. Yet he is not among the 12 MPs considering a break with Labour. On the face of it, this seems inexplicable: why remain in a party led by someone you consider beyond the pale?

The only explanation is that he (and others who hold a similar view) has not accepted that Corbyn is here to stay. It’s another strange point of agreement with some loyalists, who feel Corbyn’s grip on the party is fragile, despite all the evidence. Accepting this fact would clarify the issue: giving loyalists a reason to adopt the IHRA definition; and opponents the motivation to leave.