BELFAST — There's little hope the U.K. and Europe's red lines on Brexit can be woven together into a compromise on Northern Ireland.

On the one hand, London insists Brexit means quitting the EU customs union.

On the other, Brussels and Dublin say maintaining a customs union is the only way to avoid re-establishing a border between Northern Ireland and the Republic of Ireland. At stake, they say, is the 1998 peace accord that ended decades of strife.

As the deadline for an agreement approaches, the stalemate is hardening and nobody sees a way out. Irish Prime Minister Leo Varadkar demands that Britain deliver a solution by late June. The EU’s chief negotiator, Michel Barnier, warned on Monday during a visit to Ireland that Britain is at serious risk of crashing over the so-called cliff edge without a formal exit treaty or transition period.

Varadkar and Barnier appeared together at an “All-Island Dialogue on Brexit” in Dundalk — just 10 kilometers from the now nearly imperceptible Irish border — to present a united front in meetings with community leaders, students and other stakeholders. But they could offer little in the way of reassurance.

“The border issue in particular has become a real source of contention and difficulty” — Irish Foreign Minister Simon Coveney

Officials fudged "sufficient progress" on the Ireland issue last December by agreeing a "backstop" that would effectively keep Northern Ireland in the customs union absent a more comprehensive agreement. But U.K. Prime Minister Theresa May has said no one in her position could accept the backstop as interpreted by the EU. She has yet to offer an alternative that Brussels regards as remotely realistic.

Adding to the grim atmosphere were signs of growing rancor on the issue within the U.K. government, and a sense of foreboding among Irish officials that London has forgotten the most important issues at stake along the border — not economics and trade, but peace among communities recently at war.

“The border issue in particular has become a real source of contention and difficulty," Irish Foreign Minister Simon Coveney told reporters.

"This is not primarily about trade, just to be clear," he said. "It's about trying to maintain the normalization that has been hard-won through decades of strife and tension and violence in Northern Ireland and the island of Ireland, where now we have free, totally seamless movement of people, of livestock, of business interests, of people back and forth to school, to visit hospitals."

Coveney said Ireland would not allow the Brexit negotiations to move forward if clear signs of a solution for the border do not emerge by an EU leaders' summit schedule for late June. He said nerves are too frayed, and local communities too anxious, to allow the issue to carry into the fall.

"Most ordinary people will talk to you about their memories of a border and not wanting to go back there, of soldiers, of barbed wire, of intimidating checks, of terrorism, of smuggling, things that Irish people do not want to revisit," he said.

"We can't allow that to happen. That's why the Irish government has to take such a firm position now ... and is why for us, the June deadline while some see it as an artificial deadline, it is far from artificial from our perspective."

The reference to a June deadline is a clear dig at the U.K.'s chief negotiator, David Davis, who last week chided Brussels for repeatedly trying to set what he described as imaginary goalposts.

Ripping open the wound

Ciaran Shannon, the manager of Duncairn Community Partnership, a group that works to soothe and improve community relations in lower North Belfast, said the conflict is still too recent for Irish citizens to gamble on the goodwill of negotiators.

"Political uncertainty is always difficult," Shanon said, adding that Brexit risked ripping open a 30-year-old wound.

"It has the potential to unravel an awful lot," he said, adding that violence persisted even after the signing of the 1998 peace accord. "It's hard to describe it. It was horrendous. There were running battles."

In Belfast, where some neighborhoods experienced near-constant violence and bloodshed during the Troubles, residents said they are mostly focused on work and school and just trying to get by.

But Brexit provides one additional, unneeded worry, said Brian McKee, a development worker at the Houben Center, a community center with two entrances, one from the Catholic side of the neighborhood and the other from the Protestant side.

"In this community you have a lot of uncertainty regarding the progress as it is, and now on top of that, we have got more uncertainty because of Brexit," McKee said. "It's just more insecurity at a time when people actually need added security."