It was just as well Theresa May more or less secured her deal with the Democratic Unionist party on Saturday evening that puts her back in power inside 10 Downing Street. Because for the DUP even prime ministers in waiting have to hold on until the religiously devout Ulster party gets over the sabbath.

Negotiations between May and the 10-seat strong, potential parliamentary kingmakers in the DUP went to the wireon Saturday night ahead of Sunday - the only day of the week when the party founded by the Rev Ian Paisley refuses on religious grounds to hold political discussions.

Ironically this agreement that has led to the DUP propping up the Tories in government is remarkably similar to the one the Irish Republic’s main opposition party operates in southern Ireland.

Down in Dublin, Fianna Fáil, the party created by unionism’s one time nemesis Éamon de Valera, offers a “confidence and supply” arrangement that keeps its rival Fine Gael party’s minority coalition in power. Now, as reported in the Guardian hours after the votes were counted in the election on Thursday night, the DUP will run a “confidence and supply” agreement of their own in London.

The DUP will back the Tory government on its next budget and prevent it being brought down by motions of no confidence. However, the DUP will decide on support for the Conservatives on other issues in parliament on a vote-by-vote basis. It is a far looser deal than a formal coalition, which some sources in Whitehall were suggesting earlier on Saturday – including inaccurate claims that the unionist party had sought the post of deputy prime minister.

There has been a mixture of anger and bewilderment within the Westminster establishment – Tory as well as Labour – over the way the DUP has suddenly become the central player in shaping who governs the UK.

The nine men and one woman who are going back to the House of Commons under the DUP banner include some who are born-again Christians and deny Darwin’s theory of evolution. They are also among the main opponents of gay marriage equality and even minor reform to Northern Ireland’s near total ban on abortion.

Yet their newest MP for South Belfast also represents the changing generation within the DUP who were brought in by its modernising leader, Peter Robinson. Emma Little-Pengelly is a barrister and a former alumnus of a US government young political leaders programme.

In Northern Ireland the DUP is led by a formidable woman whose early years were forged in the sectarian ferocity of the Troubles. As a young girl, Arlene Foster saw her father, a part-time police officer, crawling through their isolated border farmhouse after he had been shot by the Provisional IRA.

Arlene Foster at the Stormont Hotel in Belfast on 9 June after Theresa May announced that she would work with the DUP. Photograph: Brian Lawless/PA

Her father survived but the experience marked her for ever and forced the family to move into a safer village in a Protestant and unionist corner of Fermanagh. The 46-year-old solicitor was herself almost killed as the IRA tried to murder her school bus driver in 1988. Having survived those kind of traumas Foster is likely to be a tough negotiator when she oversees the team established to hatch a deal with the Tories.

Among the price for supporting a minority Conservative government will be commitments from May that there will be no poll on Irish unity and that no hard border is imposed on the island of Ireland. Foster and her party did back a Brexit vote last year but have publicly stated that they are opposed to customs posts, border installations and roadblocks. Yet while her party is unashamedly socially conservative the DUP will avoid including any controversial social policies such as opposition to gay marriage or abortion in its shopping list of demands to the Tories, party sources said.

The DUP will argue that controversies over gay marital equality and abortion can only be dealt with in a Northern Ireland context by the Stormont Assembly in Belfast and are irrelevant to their negotiations with the Tories at a national level. The party will insist as well that there should be no new checks at English, Scottish or Welsh ports and airports on any citizens travelling from Northern Ireland into the UK after Britain exits the EU.

DUP sources said the list of demands would be similar to its 2015 “Northern Ireland” plan, when the party expected there to be a hung parliament and laid out its price for supporting a Tory or Labour administration.

That plan included demands for extra capital spending and more cash from the UK Treasury for spending on Northern Ireland’s schools and hospitals.

Also among the DUP’s shopping list of demands to prop up a Tory government will be either a 50% cut or the total abolition of air passenger duty in Northern Ireland, the Observer understands

On the other side of the Ulster political divide, meanwhile, the Sinn Féin president Gerry Adams said that in the light of his party capturing seven Westminster seats a referendum on Irish unity was now inevitable. “One thing we can say for certain, there is going to be a referendum on Irish unity. I can’t say when, but there is going to be,” Adams said.

Adams’ party won seven seats but Sinn Féin will continue its policy of boycotting Westminster and will therefore have no say in the formation of a new government in London.

One Northern Ireland election expert, however, disputed Adams’s claim this weekend that there was growing support for a poll on Irish unity.

Nicholas Whyte, visiting professor at the University of Ulster, pointed out that the gap between unionists and pro-united Ireland/nationalist parties has widened since the Assembly elections back in March.

Whyte said the combined pro-union vote, even excluding the cross-community Alliance Party, stacked up to around 48% while the Sinn Féin and SDLP vote together was about 41.1%. He said this marked an increase in the unionist vote over last four months.

He added: “If you factor in that most Alliance voters would plump to stay in the union with the UK in a border poll then the pro-union vote is well over 50%, so there appears to be no desire for an Irish unity referendum.

“What you must also remember is that every opinion poll on staying in the UK or leaving for a united Ireland shows that support for remaining in the union is far higher than support for unionist parties. There appears to be no majority in favour of a united Ireland or a pressing demand for a border poll.”