Even separately, Brexit and the DUP are complicated – taken together, they have proved incomprehensible to many.
Among myriad misunderstandings about the party which now holds the balance of power in the House of Commons, arguably the most fundamental is that the DUP wants a ‘soft Brexit’.
From respected newspapers such as the Financial Times (the DUP “is insisting on a soft Brexit...in return for its support of a minority Conservative government”) to star columnists such as Polly Toynbee (“DUP top priority will be soft border, saving Good Friday agreement and free movement across boundary. That absolutely rules out hard Brexit”), there is a persistent belief that the DUP is likely to take the hard edge off Theresa May’s plans to sever ties with the EU.
Even the French Government-owned France 24 channel reported that Arlene Foster “has been a vocal advocate for keeping Northern Ireland within the single market”, while the Irish Government’s foreign minister (since reshuffled) Charlie Flanagan said a month ago that the DUP “seems to me to be suggesting a soft Brexit”.
Unfortunately for those who want to see the UK retain as many parts of its EU membership as possible, they are unlikely to find many allies in the DUP.
The misunderstanding probably stems from confusing the DUP’s aspiration for a soft border for a desire that there will be a soft Brexit – a phrase which is itself ambiguous.
Among the DUP’s MP group are some of the most enthusiastic and committed Brexiteers in Parliament, politicians who on the issue of Europe identify more with Ukip and the right of the Tories than with Ken Clarke or Nick Clegg.
This is a party whose founder, the late Ian Paisley, believed that “Satanic power” held the EU together and who, when first elected to the European Parliament in 1979 (where he viewed himself as being “among a lot of frog-eaters and snail-mongers”) famously pledged to “milk the EEC cow dry before slitting its throat”.
Since then, the DUP’s arguments against the EU have become more mainstream – sovereignty, red-tape, immigration – and that allowed the DUP to virtually run the Leave campaign in Northern Ireland, seconding the party’s respected director of policy, Lee Reynolds, who alongside another colleague, Ruth Maxwell, ran Vote Leave in Northern Ireland (where despite a majority voting to Remain, the 56%-44% result was much closer than many observers expected).
The DUP’s Westminster leader, Nigel Dodds, was on the 17-strong board of Vote Leave, as was its Westminster chief of staff, Christopher Montgomery. Mr Dodds – who speaks fluent French and once worked as an aide to Dr Paisley in the European Parliament – has been a consistent supporter of leaving the EU.
When I asked the DUP about its position on a soft Brexit, they directed me to comments in the Commons a fortnight ago by Mr Dodds, who said: “Let me make this very clear. I believe that when people voted, in the European Union referendum, to leave the European Union, they voted to leave the single market and the customs union, and I believe that Northern Ireland, along with the rest of the United Kingdom, must do likewise.”
Since then, two other senior DUP MPs – former finance minister Sammy Wilson and Ian Paisley, son of the party’s founder - have explicitly spelt out in the Commons chamber that they want out of both the single market and the customs union, with Mr Paisley saying that it is “absolutely crucial that we leave the customs union”.
Last month Richard Bullick, who until June was the strategic brain of the DUP and Mrs Foster’s key adviser, told Radio 4’s Today programme: “The DUP policy has been that the UK should leave the Customs Union at the same time as it leaves the European Union, so I don’t see that an argument is going to be put forward that the UK should stay within the Customs Union”.
Mr Bullick’s comments are particularly significant. Not only has he – alongside de facto chief of staff Timothy Johnston – been at the beating heart of the DUP for more than 15 years, but he is one of the most liberal members of the DUP and rumoured to have been on the ‘Remain’ wing of the party.
So if the DUP doesn’t want a soft Brexit, how can it achieve a soft border? The answer is far from clear. Already, the DUP has deployed the argument that if there is a hard border it will not be at the behest of London or Northern Ireland – who both want to keep it as low key as possible – but on the orders of Brussels.
What is clear is that the firmest red line – as Arlene Foster told me last year – is any possibility of cutting Northern Ireland off from the rest of the UK, either through customs checks or passport control.
The nightmare for the DUP is that having backed Brexit it finds that Northern Irish people have to produce their passport to travel within their own country and they have secured the agreement of the Prime Minister that such a scenario will not develop.
If the ultimate choice for the DUP is a hard border at the Irish border or a hard border at the Irish Sea, they will unquestionably choose the former every time.
The party’s manifesto pledges on Brexit were aspirational rather than detailed, something which senior DUP members say is because so much of the detail is consequential – for instance, if the UK opts to stay in the Single Market, its has implications in a host of other areas.
But there is also a tension – thus far, publicly unseen – within the DUP. Some in the party did not even support Brexit, fearing that it would lead to the constitutional uncertainty which has the potential to destabilise what had been Northern Ireland’s fairly settled place within the Union.
Sky News’ political editor Faisal Islam picked up on this, reporting last month that “different DUP sources say different things about the approach to Brexit”.
That is in keeping with the fact that not all in the DUP backed Brexit to begin with. At least one DUP minister is known to have been in favour of Remain and the DUP leader took a long time to firmly state that the DUP would be campaigning to Leave.
Unlike the SDLP and Sinn Fein, which from 2015 had been stating that they would campaign to Remain, Mrs Foster waited until February 2016, when David Cameron’s renegotiation with Brussels was complete, before picking a side – something which implied that if Mr Cameron had come back with more then the DUP could have supported a Remain vote.
There is another fascinating detail in that period which may be a portent of what is to come: For months prior to Mrs Foster announcing what way the DUP would go, some of her MPs – particularly Mr Paisley and Mr Wilson (who was campaigning alongside Nigel Farage) – took positions which indicated that the party’s stance would always be to back Leave.
Now it is again the MP group which is most vocal and most specific about leaving the customs union and the single market - issues about which Mrs Foster, who has called for a “sensible Brexit”, has been far vaguer.
The DUP no longer bases its Euroscepticisim on its founder’s fundamentalist religious certainties and the party these days is a pragmatic negotiator.
But – as evidenced on Wednesday as the DUP celebrated the defeat of a European Parliament motion seeking special EU status for Northern Ireland after Brexit – this is a party which is ideologically opposed to the EU and fearful that attempts to soften Brexit will undermine Northern Ireland’s place within the one Union about which they are passionate – the Union of Great Britain and Northern Ireland.