LONDON — In the days of the Troubles, as the 30-year sectarian conflict in Northern Ireland was known, the borderlands between the North and the Republic of Ireland were called “bandit country” — a frontier of milk smugglers, gun runners and frequent clashes between British soldiers and Irish Republican Army cells.

Today, because the sides made peace and because both the Irish Republic and Northern Ireland are members of the same European Union, the border between them is wide open to the point of invisibility. Manufactured goods, alongside tens of thousands of people, and a lot of sheep and Guinness stout, pass freely on a daily basis, without customs checks or passport control, over new highways, farm roads and country lanes.

But that border is now a major point of contention in the Brexit debate, as Britain and the E.U. sort out how to disengage next year.

European negotiators on Wednesday released draft language for a treaty that would have Northern Ireland essentially remain in the E.U. customs union, which would allow for an open border for trade and travel between Northern Ireland, still a part of the United Kingdom, and the Republic of Ireland in the south, a member of the European bloc.

In Parliament, British Prime Minister Theresa May immediately called the proposal unacceptable, signaling a rocky road ahead.

May said the Brussels draft would “undermine the U.K. common market and threaten the constitutional integrity of the U.K. by creating a customs and regulatory border down the Irish Sea, and no U.K. prime minister could ever agree to it.”

Presenting the proposed treaty, Brussels’s chief negotiator Michel Barnier said that Europe was open to other suggestions but that it must preserve the open border. He signaled that Europe needed to hear clear answers from May and that time was running out.

This vexing issue of the Irish border was hardly mentioned before Britain’s historic June 2016 vote to leave the European Union. 

But the balance between Republicans and Unionists, and between north and south on the Irish island, remains fragile and unsettled 20 years after the sectarian violence ended with the Good Friday Agreement.

May is squeezed by the border issue in part because she failed to achieve a majority in the last British elections and so had to enter into a soft coalition with the Democratic Unionist Party (DUP) of Northern Ireland, made up of Protestants loyal to Britain and the monarch, who oppose any move that would sever ties with the United Kingdom.

The DUP leader in Parliament, Nigel Dodds, on Wednesday described the latest E.U. proposals as “ludicrous” and said that if enacted, the treaty would be “catastrophic” for Northern Ireland.

“We did not leave the European Union to oversee the breakup of the United Kingdom,” he told the BBC.

The conservative Times of London wrote, “The European Union has demanded that Britain effectively hand over sovereignty of Northern Ireland to Brussels if it cannot find a solution to the Irish border question.”

Meanwhile, the Republic of Ireland’s foreign minister, Simon Coveney, praised the draft language. 

May has suggested the Irish border issue can be finessed with a combination of clever compromise and 21st-century technology, but she has not said how.

The question of what to do about the border was dismissed this week as a nonissue by hard-line Brexiteers in May’s cabinet, foremost by Foreign Secretary Boris Johnson, who on Tuesday suggested the solution was no more complex than arranging cameras along the frontier to take pictures of license plate numbers passing by, to collect tolls and information.

He compared the Irish border to moving between two boroughs in London, between zones where traffic tolls are taken to reduce congestion and pollution in the city’s center. Johnson’s comments, criticized as glib and ahistorical, angered both sides of the Irish border.

Returning from a morning jog in the snow, Johnson, a former London mayor, told reporters Wednesday, “What is going on at the moment is that the issue of the Northern Irish border is being used quite a lot politically to try to keep the U.K. in the customs union, effectively the single market, so we cannot really leave the E.U. That is what is going on.”

Earlier this week, Jeremy Corbyn, leader of the Labour Party and the opposition in Parliament, said he supported a softer Brexit that could include a customs union with Europe on trade and tariffs — an arrangement that could preserve an open Irish border but would block Britain from making its own bilateral deals abroad. May dismissed the idea.

The prime minister is scheduled to present the government’s vision for Brexit in a major speech on Friday.