At some point, we will need new words for “remainers” and “leavers”. They are legacy terms from a one-off campaign that will, on Brexit day, become obsolete. Does remain then become rejoin? Will leavers turn into stay-outers? Or perhaps the labels will outlive their original function. It happens. People who describe politics in terms of “left” and “right” aren’t talking about seating arrangements in the French national assembly at the end of the 18th century, although that is where the categories were born. I doubt that the Brexit brands will be so durable, or mutate so far, but they have come a long way already.

Remainer is the more elastic of the two. It applies to full-throttle revanchists who campaign to dispose of Brexit altogether. But it is also used for soft-leavers in the cabinet who have signed up to Theresa May’s negotiating agenda, and that doesn’t involve much remaining at all.

Beyond Westminster, there is a tenuous link between domestic Brexit tribes and the institutions commonly (and inaccurately) called “Brussels”. Some ideological Eurosceptics read the treaties before denouncing them, but they are a minority of leave voters. Most wanted rid of the European Union for less precise reasons.

Remainers and leavers accuse each other of exaggerated passion – naively romantic or aggressively paranoid – for concepts that are only tangentially connected to the actual EU. Both are right. Britain’s membership of the club has become a proxy for culture wars fought on multiple fronts: immigration, globalisation, environmentalism, even penal policy. Attitudes to capital punishment and multiculturalism were a better predictor of people’s attitudes towards the EU in 2016 than whether they voted Labour or Tory in previous elections.

A misalignment of party allegiance and territorial strongholds in the Brexit culture war is wreaking havoc with conventional political models. That, in part, was the story of last week’s local elections. It doesn’t matter to leave voters in, say, Amber Valley, that Jeremy Corbyn endorses the referendum outcome. His party hums with the socially liberal, metropolitan cultural vibrations of Brexit-bashing London. So Labour did fine in the capital and other big cities, but struggled to capture more provincial targets.

Many of the Tory high priests of Brexit style themselves as liberals. Boris Johnson is much more relaxed about immigration than May. Michael Gove is waging a millennial-friendly war on discarded plastic. But a Govian eco-Brexit doesn’t impress remain voters in Richmond upon Thames, who see it as a green patina only recently formed on the roof of a church whose patron saint is Nigel Farage and whose guiding creeds are social conservatism and reactionary nostalgia.

Many Tory leavers resent that characterisation. But if they didn’t want their image contaminated by bitter intolerance, they should have been more careful about the company they kept in the referendum campaign, and the racially tinted messages they borrowed. Besides, backbench Eurosceptic hardliners keep the flame of nationalist grievance roaring because it burns bridges to Europe so much more efficiently than their own rarefied arguments about regulatory divergence.

Jacob Rees-Mogg would not have as much purchase on the current debate over customs regimes, for example, if it were framed as the quest for a technical solution to a problem raised by May’s commitment to a very hard version of Brexit (which it is). His voice is amplified by culture warrior megaphones, rallying leave partisans to defend the one true Brexit against treasonous counterfeits.

That dynamic is hardwired into the whole project. There is a mismatch between leave culture, which thrives on heroic simplifications, and leaving in practice, which is a labyrinth of unheroic complications. The deeper into the maze May plunges, the harder it gets for those who campaigned with promises of a swift and easy escape to express sincere satisfaction with the final product. Many Tories will decide that any Brexit is better than none. They will murmur their assent to May’s deal and, once Britain has been bundled out of the EU, agitate for new leadership. They will not reject May’s Brexit, but nor will they rush to own it.

That is because none of the advertised benefits of leaving the EU will materialise. Leavers will experience total victory in the political battle over EU membership, but without equivalent advances in the culture war. May’s deal will not accelerate reconciliation between a younger, liberal generation that feels its future has just been vandalised by its angry elders. And, over time, the brutal logic of human mortality favours the junior cohort. I don’t like the ugly, ghoulish habit that some remainers have of mapping a route to pro-European majorities through the graveyards of ageing leavers. Still, the underlying demographic observation is not entirely false.

A less macabre observation in the same vein is that the historical trend is for British provinces to look and behave more like the big cities, not the reverse. In terms of social attitudes, where London goes, Nuneaton follows. And when politics is consumed by culture wars, that is bad news for the Tories, even if Brexit passes without economic calamity.

The remainer tribe isn’t going to renounce its metropolitan mores just because the cause of remaining in the EU is lost. And the leaver tribe, upon leaving, will cling to grievances that were channelled against Brussels but not caused there. Neither side will cherish May’s messy deal and, because it will be unloved in the country, few MPs will have much incentive to defend it.

There may be no shortage of will to deliver Britain out of the EU now, but in time there will be a great washing of hands and collective denial of responsibility for the deed. Brexit is the adopted child of a whole generation of politicians. It will be an orphan one day.

• Rafael Behr is a Guardian columnist