On Monday, Northern Ireland’s health minister Jim Wells resigned after he made numerous comments that not only disparaged gay and lesbian parents but alleged that LGBT parents were more prone to child abuse.

His party, the Democratic Unionist Party (DUP), is the strongest party in Northern Ireland today, and its leader, Peter Robinson, serves as Northern Ireland’s first minister. Though Northern Ireland is home to just 2.9% of the United Kingdom’s population, and it’s allocated just 18 seats in the 650-member House of Commons, those seats could make the crucial difference in the race to become prime minister.

Though the election has been more about Scotland’s role in any post-election coalitions, Northern Ireland could become even more important. If Robinson’s DUP holds the balance of power, it could thrust one of the most anti-gay, socially conservative parties in Europe into the spotlight with consequences that could shake the still-fragile power-sharing agreement that’s brought peace to Northern Ireland.

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Polls consistently show three things:

• The Scottish National Party (SNP) is projected to win, for the first time, the vast majority of Scotland’s 59 seats, and its leader, Scottish first minister Nicola Sturgeon has said she’ll prop up a center-left government led by Labour’s Ed Miliband and will not support, under any circumstances, any vote of confidence for the incumbent, David Cameron (pictured above with Robinson).

• Neither the Conservatives nor Labour are projected to win enough seats to form a majority, forcing Cameron and Miliband to seek allies from minor parties.

• The Liberal Democrats, which have joined the Tories in a governing coalition since 2010, and whose leader, Nick Clegg, says he could support either the Tories or Labour after 2015, are not projected to win enough seats to propel either major party to a majority.

Conceivably, that’s where the DUP would become vital — a world where a Tory-Lib Dem coalition falls just short of the 326 seats Cameron would need for reelection. No other party, after the SNP, is projected to win more seats than the DUP, which currently holds eight of Northern Ireland’s seats.  After entering into an electoral alliance with the Ulster Unionist Party (UUP) in a handful of constituencies, there’s reason to believe that the DUP/UUP could together emerge with as many as 10 seats.Even though the eurosceptic United Kingdom Independence Party (UKIP) is expected to win between 10% or 15% of the vote nationally, its support will be dispersed over the entirety of Great Britain, a disadvantage in a first-past-the-post system of 625 discrete constituencies. The DUP, to the contrary, won just 0.6% of the national vote in 2010.

The DUP was founded in the early 1970s by Ian Paisley, a Protestant evangelical minister, and he brought to his ministry and to the DUP a fundamentalist’s fervor, and Paisley and the DUP routinely refused to work with Catholic republican groups like Sinn Féin, thereby prolonging the sectarian violence that plagued Northern Ireland for years. When Paisley did assent to a final peace accord, it opened the way for the Northern Irish parliament’s restoration at Stormont, where the DUP governs in a power-sharing arrangement with Sinn Féin and smaller parties.

The DUP’s relative gains against the UUP came in parallel with the more radical Sinn Féin’s gains against the more social democratic Social Democratic and Labour Party (SDLP) in Northern Ireland. Unlike the SDLP, Sinn Féin, which seeks a reunified Ireland, refuses to sit in parliament in the House of Commons.

It’s not the first time a Conservative government has looked to Ulster unionists to bridge the gap in the House of Commons. Between 1995 and 1997, when prime minister John Major lost his majority in the final days of a 18-year stint of Tory rule, he relied on the UUP.

But the DUP has always been more populist and more socially conservative than the UUP, and it has traditionally appealed to working-class Protestants in Northern Ireland. With the UUP’s longstanding ties to the Conservative Party nationally, the DUP has been closer to Labour in recent years, even though the DUP is to the right of even UKIP on issues like LGBT rights and abortion (which is still illegal in Northern Ireland).

Robinson, has said that he is willing to work with either the Tories or with Labour. Here’s what Robinson told The Economist earlier this week about the DUP’s demands:

We don’t expect to get everything in our plan but if we are having discussions with two potential government parties we’d look at how much of our plan each of them are prepared to assist us with. And look at their programme for government as well and on that basis we’d make a decision. It’s as simple as that.

It’s easier to imagine the DUP propping up a Cameron-led coalition. Even last year, with an eye on coalition-building, Cameron invited DUP officials to a reception to build closer ties. Nevertheless, after spending the campaign arguing that a SNP-supported Labour government would amount to a ‘coalition of chaos,’ it would be somewhat hypocritical of Cameron to turn around and align the Tories with the DUP. The obvious difference, as Cameron would surely note, is that the DUP is a unionist party, unlike the SNP, which exists primarily to boost the cause of Scottish independence.

But for the prime minister who legalized marriage equality in England, despite the opposition of many Tories, it will make an awkward shift to embrace a party that is well-known for its ‘Save Ulster from Sodomy’ campaign in the late 1970s.

The DUP’s participation in government could also destabilize Northern Ireland in unknown ways. It would give the DUP much more power vis-à-vis the other parties in Northern Ireland. If Robinson and the unionists used their leverage to boost funding for Northern Ireland as a whole, a Westminster deal could solidify the gains of the past two decades. But if the DUP tries to advance its ideological priorities or prioritize projects in Protestant areas of Northern Ireland at the expense of Catholic areas, it could rupture the region’s fragile balance.