Dotted around Labour conference in Liverpool are T-shirts bearing the slogan “Love Corbyn, Hate Brexit”, which is not an unusual combination but an increasingly unstable one. It is meant as a declaration but comes across as a plea – urging the leader to reward the devotion of his fans with a sign that he shares their pain at the prospect of leaving the European Union. He doesn’t.

Jeremy Corbyn’s attitude towards Brexit is not mysterious. He was a critic of the EU before the referendum, declared himself a tepid supporter of membership during the campaign and showed not a flicker of sorrow at the result. Despite emotional aversion to Brexit among Labour members, the leader is up for leaving.

Campaigners pushing for another referendum forced the issue on to the agenda in Liverpool, but in terms of policy change they got only a foot in the door. It was decided after hours of haggling that the second-vote option should be left “on the table” if the party’s preferred outcome – a general election – doesn’t materialise.

Some of Corbyn’s oldest allies then made it clear that a plebiscite should exclude the option of remaining in the EU on current terms. Len McCluskey, the leader of the Unite union, and John McDonnell, the shadow chancellor, have both said the rival proposition to a Brexit deal would be exiting with no deal. But it is also Labour policy to “vigorously” oppose no deal and to vote against the Brexit that Theresa May is trying to negotiate. The absurd equation is that the opposition is against May’s deal, against no deal, but not against a referendum inviting people to choose between May’s deal and no deal.

Much of Labour’s difficulty flows from the problem of appealing both to the current, pro-EU supporter base and a different, target electorate in constituencies that voted leave. The best defence of Corbyn’s position is that many of those Brexit backers thought they were delivering a once-in-a-generation ballot-box boot to the political class. Quitting the EU makes practical remedies harder to deliver for those people, but that is not an easy pitch. There is a noxious hauteur in telling people the thing they wanted is not what they really needed.

The riposte is that politicians who see a national calamity unfolding have a patriotic duty to avert it. If voters are unpersuaded that Brexit is a mistake, the task is better persuasion, not surrender to the error. Corbyn’s most vaunted skill is meant to be evangelism. He is credited with single-handedly shifting Britain’s political centre of gravity leftward. If his magnetism really works as advertised it could surely be deployed to reorient European debate. But that never happens.

The reason is not electoral calculus but allergy to defence of the status quo. There is a strain of Corbynism that is hostile to the set of postwar institutions that were bulwarks of the “west” during the cold war and, after it, upheld a hegemonic capitalist world order. In radical left demonology they are instruments of imperialist exploitation. The EU is not a prominent monster in that villainous hierarchy – it is no Nato or World Bank – but it is a member of the same extended family. It is not something leftists in the Corbyn-McDonnell-McCluskey mould instinctively defend.

What makes this awkward in relations with younger and less doctrinaire Corbynites is that in 2018 the prominent challenge to that western institutional order comes from the far right. For many Labour people, Brexit was one of twin traumas in 2016, the other being Donald Trump’s election. The most effective insurgency against the European status quo today is racist and nationalistic. And so, regardless of any noble interior motive, the practical result of tagging along with an anti-EU project is tactical alignment with a wrecking enterprise that has Steve Bannon as its guru, Boris Johnson as its British proconsul and Russia as its immediate strategic beneficiary.

Corbyn’s team will never recognise in themselves a symmetrical alt-left to the “alt-right” menace they revile. The two tribes envisage very different end-states. But there is between them a cultural affinity in the romantic fantasy of creative destruction; a similar quickening of the pulse at the prospect of the old order crumbling. Tory Brexit-pushers and Labour Brexit-enablers both have an ear for the music of breaking glass and a shared secret: their plans require things to get worse for most people before anything would get better.

None of this means that Labour’s European position is settled. The leader’s team likes power more than it dislikes the EU and is capable of pragmatism. It is mindful of the “Love Corbyn, Hate Brexit” crowd and if it looks as though pro-remain feeling is cannibalising affection for the man they call just “Jeremy”, he will shift.

But there is also a looming scenario in which the UK crashes out of the EU, causing chaos and misery, for which the Tories get all the blame. Labour then scoops up the votes of the immiserated. It isn’t a position that anyone around Corbyn will express out loud because it sounds brutal and cynical: no one will trumpet a plan of complicity with Conservative no-deal maniacs to engineer a crisis in the hope of capitalising on public pain. The Tory right and Labour left are supposed to be miles apart on the spectrum, diametrically opposed foes. But that doesn’t mean they have nothing in common – only that they have no interest in drawing attention to the common ground between them.

• Rafael Behr is a Guardian columnist