For a few weeks it was all going well for the so-called remain alliance. As Boris Johnson strained every sinew to facilitate the most damaging Brexit possible, bitter opponents Jeremy Corbyn and Jo Swinson teamed up with other party leaders to force, in law, a request to extend the process. They then agreed not to sanction an early election, against Corbyn’s natural instinct and arguably his party’s immediate interests. And then the truce broke.

No sooner had parliament been prorogued than the centre and left parties forgot they were meant to be working together against a near-existential threat. The old rivalry resumed in earnest. Labour denounced the Liberal Democrats for their new “extreme” policy of seeking to revoke article 50 without a referendum. Swinson accused Corbyn of “betraying” remain voters for not personally committing to remain in a referendum.

The allegation that Corbyn has betrayed remainers is not just untrue: it reveals a problem at the heart of the entire Brexit debate.

Corbyn remaining neutral in a referendum would represent a compromise and not a betrayal

First, the facts. Corbyn’s position on Brexit has transformed over the past two years. At the time of the 2017 general election Labour was not committing to the single market, customs union or even a transition period. Now it guarantees a referendum that will, in all circumstances, include an option to remain in the EU. It is a curious form of betrayal that offers the people being betrayed exactly what they were demanding.

This is, of course, not to spare Corbyn legitimate criticism. Labour’s path to this referendum pledge has been slow and tortuous. Its language has been consistently murky and ambiguous. The long-standing policy of triangulation has confused and alienated both leavers and remainers. Even now, many voters are bemused by the notion that the party might renegotiate Brexit and then campaign against its own deal. Corbyn’s refusal, at this stage, to personally endorse either option has provoked further opprobrium.

The problem for Corbyn is that his tactics are at the same time sensible and unsustainable. It is entirely reasonable to seek to adapt a Brexit deal to suit his party’s priorities before putting that to the people, yet on the doorsteps it could sound ridiculous. It is, furthermore, a respectable ambition to stay above the fray during a profoundly divisive referendum campaign, but also absurd that a government might call a vote of such generational importance and not adopt a firm stance in either direction.

It is, in the end, inconceivable that Corbyn could remain officially neutral for a referendum. A Labour-led government would be compelled by its members and voters to support remain, and its leader could not diverge. But even if he did, that would represent a compromise and not a betrayal. Our fundamental problem is we have lost the ability to distinguish between the two.

We now confront a situation in which language proves as dangerous as policy. On an immediate level, Lib Dem characterisations of Corbyn’s position as betrayal makes necessary cooperation much harder. Both parties risk losing sight of their real and common opponent. Labour and the Lib Dems are each offering a route to remain. If they focus their energy on attacking each other, they could facilitate both a Tory majority and no-deal Brexit.

The more chronic problem is the systematic poisoning of our national discourse. Politicians can no longer merely disagree. They must be acting in bad faith, or subverting democracy, or betraying the electorate. This finds its extreme form in the word “treason”, which now peppers and pollutes the language of rightwing politicians and commentators. But it has also insinuated itself into the way we address Brexit altogether.

The essential toxin here is the requirement for political purity. This is partly driven by the increasing radicalism of our mainstream political parties and partly by the appetite for nationalism unleashed by the referendum and now rapidly advancing. We have almost reached the stage where all voters should demand exactly what they want, exactly how they want it.

Every Brexit outcome has always constituted a betrayal of leavers, because in 2016 Vote Leave outlined multiple contradictory outcomes, none of which could be implemented in reality. Now any referendum involving Corbyn must constitute a betrayal of devoted remainers, because he will never be as enthusiastic about the EU as they are.

Corbyn has made no secret of attempting to reconcile leavers and remainers. It is legitimate to criticise his approach, and he may well fail. The real problem is not his attempt to bridge divisions but the fact such an attempt now feels impossible.

In truth, Britain is no longer just riven politically and economically, but fully entrenched in a culture war which demands rigid and extreme conceptions of identity. This new polarisation necessitates an all-or-nothing stance not just on Brexit, but on politics altogether. When we join battle on those lines, we leave no room for anything in between or any obvious route to heal afterwards.

A referendum with a viable Brexit and remain option will anger some voters but betray none. Ultimately, the only things at risk of being betrayed are our tradition of tolerance, and our liberal democracy.

• Jonathan Lis is deputy director of the thinktank British Influence