The 1998 Good Friday Agreement - a major development in the Northern Ireland peace process - commits the United Kingdom and Irish Governments to demonstrate "rigorous impartiality" in their dealings with the different political traditions in Northern Ireland.
Although the DUP are unionists - wanting to remain part of the United Kingdom - and broadly support numerous policies of the Conservative and Unionist Party (as the Conservatives are correctly called), May's proposed deal could scupper attempt to broker a power-sharing deal with Sinn Fein - which promotes the unification of Ireland - on the Northern Ireland Executive.
The proposed deal would see the DUP back the Conservatives in votes on the Budget and confidence motions.
There have been concerns, raised by a range of politicians from Irish Republicans in the left-wing Sinn Fein party which is active throughout Ireland to the Conservative former prime minister John Major, that May's government could not play the role of "honest broker" in talks in Northern Ireland if it has formal ties with the DUP.
"Everything is all over the place", said a senior executive responsible for Brexit preparations at a FTSE 100 company.
Barnier dismissed the suggestion of postponing the negotiations and said such a delay would only prompt further instability.
How Ireland will look post-Brexit could be one of the most sensitive subject of the upcoming talks.
Nor has May seen Northern Ireland as a priority; prior to this week's meetings the extent of her engagement was to visit the Balmoral Show during the general election campaign.
Cei,ok ius soli. Lega,pensate a italiani
Questo è pericolosissimo: "inseguire qualcun altro solo per rincorrere il successo vuol dire non fare politica, ma fare soltanto il proprio interesse".
Where does all this leave the DUP and can it exert influence?
Former cabinet minister, Michael Portillo, said the Prime Minister "didn't use her humanity" when she visited the scene of the fire yesterday.
Mr Hanson, who was a part of the Labour negotiating team that helped secure the St Andrews agreement - concerning devolved powers - in 2006, said despite concerns over the DUP's stance on issues such as abortion and LGBT equality, the focus will be on the bigger programme of government.
DUP sources also stressed the importance of everyone in Northern Ireland "owning" whatever concessions the party specifically wins for the region in its discussions with the Conservatives.
"The consensus expectation was for an nearly unanimous decision to keep rates unchanged, however in an unexpected development we got a significant split open up amongst policymakers about whether to hold or whether to hike rates".
Previous Northern Ireland executives have wanted to bring it down to 12.5% to match the corresponding rate in the Irish Republic.
Foster also said a deal on power-sharing in Northern Ireland is "very likely" this month, according to RTÉ.
He stressed the objectives of ensuring that Brexit does not impact negatively on the Good Friday Agreement and the peace process there, and protecting North-South trade and economic activity and the Common Travel Area.
Northern Ireland has enjoyed peace and prosperity for a long time now let us hope this continues.