The Democratic Unionist party is defined by its hostility to the Republic of Ireland. For the DUP the political crisis of Brexit has generated a once-in-a-lifetime opportunity to take back control of Northern Ireland. It seems that it will do this even if it entails destroying the Good Friday agreement and defying the wishes of a substantial majority of its own electorate.

This is evident from the remarks of the party’s leader, Arlene Foster, on the fringe of the Tory party conference this month. The 1998 agreement is not “sacrosanct”, she said, and “could evolve” into something different in the context of the UK’s departure from the EU. Foster also told a sympathetic newspaper how it was “deeply frustrating to hear people who voted remain and in Europe talk about Northern Ireland as though we can’t touch the Belfast agreement”.

Earlier in the year the party had sought to use its leverage in the Commons to rework legislation which the responsible minister said was “a cornerstone of the Belfast agreement”.

None of this should be in the least surprising. The current leaders of the party founded by Ian Paisley are defined by the break he made with mainstream unionism over the Good Friday agreement – it is the DUP’s main calling card, the reason it has successfully crushed the rest of political unionism. Under its “leadership” the devolved structures of government created by that agreement have ground to a halt. And to make matters worse various cross-border initiatives, both fostered by and developed since it came into effect, are now threatened by the hardest of hard borders that the DUP’s Brexit fanatics at Westminster (a cult within a cult) seem determined to embrace. The electoral lottery has awarded the DUP a potential prize it seems determined to claim. Ireland’s defeat is their victory even if, as with Shelley’s Ozymandias, “nothing beside remains”.

It has been reported that Theresa May refuses to meet with Northern Ireland’s non-unionist political representatives as a group. The four political parties that requested a joint meeting – Sinn Féin, the SDLP, the Alliance, and the Green party – represent a remain opinion in Northern Ireland that delivered a strong vote for the EU in the 2016 referendum.

In the local elections for the ill-fated devolved assembly that followed in 2017, the DUP failed to secure a majority of voters within the region – it managed only 28% of first preferences, as against the 51% combined total of the four parties that the prime minister will not meet. In the general election shortly afterwards the shares were DUP 36%, the four 50%. The leader of the previously hegemonic Ulster Unionist party, Robert Swann, said last week that the DUP had taken unionism “into the gutter”. At his first conference as leader the year before he had warned that a “hard border” was not an option during free trade negotiations, and that a badly handled Brexit created a “real danger of returning to the politics of the past”.

Northern Ireland business agrees: local CBI chair Trevor Lockhart recently wrote to May on behalf of 21 signatory organisations warning of the grave concern felt by business at the prospect of a no-deal Brexit, now coming much more plausibly into view in light of the refusal of any compromise on the Irish backstop – a position rendered intractable by DUP intransigence. Lockhart, who admits that he may himself have to move his business south to the Republic of Ireland, is clear that (as he told the Financial Times) the concerns felt by business are “cross-sectoral and … cross-community”. That point is further attested to by opinion polling in the province published by Queen’s University Belfast in July.

With its opposition to Brexit combining with its views on the rights of women, gay people and much else, the DUP undoubtedly presents to many in Britain as an absurd throwback to a nasty time of sectarian politics and evangelical reaction. Views towards it in the Republic of Ireland are probably the same; indeed the state has liberated itself from a conservative Catholic dominance whose social policy priorities are now to be found (irony of ironies) only within the ranks of the Rome-hating DUP. It cannot be stated often enough that this is also how the DUP present to very many in Northern Ireland as well, perhaps (as the numbers above indicate) even a majority.

It was the 17th-century Protestant preacher Thomas Fuller who seems to have been the first to say that “the darkest hour is just before the dawn”. It has been so in the Republic, where reaction to a series of awful events and discoveries about the past helped propel the country to its brighter present. Brexit has pushed the non-unionist parties into important progressive alliances: on business, the border and rights (the last of these especially vulnerable after Brexit). Might the crisis of Brexit be about to present Northern Ireland with a chance to transcend the ancient green-orange divide?

May should meet with the Northern Ireland remain parties with more votes than their DUP opponents, and throw in Lockhart and Swann for good measure. It will at very least make a change from dreary exchanges of red lines with the 10 DUP MPs to which she is beholden. And she might even be able to spot a nascent Northern Ireland in the making: one that is warmer, more tolerant and connected to the wishes of its people than its supposed representatives.

• Conor Gearty is professor of human rights law at the LSE, and a fellow of the British Academy