I'll try and make a rough comparison here to a fringe movement within Irish Republicanism called "legitimisim". If you're not familiar with it, then I'll try not to drone on too much about it and just get to the main points...
* The 1918 UK General Election was the last to include all of Ireland, with Sinn Fein winning 73 seats. However they had a policy of abstention from Westminster and instead formed the First Dail Éireann in Dublin following from their manifesto commitment. All MPs elected to Irish seats in the 1918 election were invited to this parliament, but only those elected as Sinn Fein members attended, and thus a "revolutionary" government was formed which sought to achieve international recognition.
* Ultimately the Irish Unionists weren't that pleased by what took place, especially those in Ulster. They & Westminster refused to recognise the rival Dail in Ireland. This led to the Anglo-Irish War which then came with the partition of Ireland. The first elections for these two separate jurisdictions (named at the time Northern Ireland and Southern Ireland) were held in May 1921 - members of the Dail decided that both elections would be used to elect a new Dail (Second Dail Éireann). The Southern Ireland election was a piece of piss for Sinn Fein as they won but all four seats uncontested (the remaining four won by unionists representing Trinity College, again unopposed) while winning five in Northern Ireland. Again only Sinn Fein members entered the Second Dail, 125 of them in total.
* Negotiations between King George V and the Second Dail saw a truce coming into effect in July 1921. Further negotiations took place between the Second Dail and Lloyd-George's government, with an Anglo-Irish treaty agreement coming in early December the same year. About a month later the sitting Dail voted to accept the treaty somewhat narrowly, 64 to 57.
* That set a chain of events of a major fall out between pro-treaty and anti-treaty factions, many anti-treaty members accusing the pro-treaty supporters in the Dail of having broken their oath to the Irish Republic under the threat of war with Britain. This led to the Irish Civil War of 1922/23.
* Over time some of the anti-treaty republicans came to accept a truce with the new Irish Free State, most notably Eamon De Valera whom left Sinn Fein in 1926 to form a new party to be elected and take up seats in the Dail of the Irish Free State, whom by the late 1930's was able to push forward a new constitution establishing the Republic of Ireland. Defections, capture & convictions by British & Free State authorities and others in exile meant that the few remaining members of the Second Dail, whom they regarded as never having been formally dissolved, declared that they had transferred their deemed authority to the IRA Army Council.
* Under this "transfer" it is held that the elections to the Second Dail Eireann were the last legitimate elections to be held in Ireland, though this never stopped the signatories of this declaration from standing in elections up until 1938 themselves, sometimes winning seats. Essentially, the IRA Army Council deemed themselves to be the legitimate government of the Irish Republic (not to be confused with the Republic of Ireland - insert Life Of Brian reference here). Because of further splits down the line in 1969 & 1986, along with statements made at the time of the sole surviving member of the Second Dail (Tom Maguire), this line of Republican Legitisism follows the line that at present the Continuity IRA Army Council is the representative government of Ireland, backed politically by Republican Sinn Fein (though there are lines within the "Provo" Sinn Fein that would still regard the Provisional IRA Army Council as being the heirs to the Second Dail).
Bit more detail on Wiki... https://en.wikipedia.org/wiki/Irish_republican_legitimism
So to cut a story short, Irish Republican Legitimism believes that there has been no proper democratic elections in Ireland since 1922 and there will be none until they regard their goals as being fully met and until then, Ireland is under a temporary but indefinite military rule. That doesn't account for their announcement being retroactive, nor understand that within almost all of Ireland they're as popular as a hot dog & bacon sandwich stand at a Bar Mitzvah (they get the rare local councillor elected, but that's about it).
Anyway. The point is that those that decry that holding either a second referendum on the matter of the UK exiting the EU or not, or what type of exit deal should be sought, on the basis that it would "endanger democracy", be undemocratic or any claim on a similar vein, are IMO following along similar lines to that of the Irish "legitimates" mentioned above in that they fell that until the result of the 2016 referendum is carried out to their satisfaction
then no further referendum or election that is UK-wide is legitimate. But of course, this ignores several conventions regarding democratic processes not just in the UK but also across most developed nations.
* A democratic decision is always subject to potential future review because circumstances in the future can significantly change from what was agreed at the time, and those agreeing then often accept that it may need to be revisited. Elected parliaments do this all the time, wherever it is a change of external circumstances that mean the original agreement can not be fulfilled either technically or in spirit, or that evidence and experience since the original agreement shows that it deserves being revisited. As an example, around 3-4 years ago a Swiss referendum passed a law to restrict immigration from EU nationals into Switzerland immediately rang alarm bells in their Federal Government because of the "guillotine clause" in the bilateral arrangements Switzerland has with the EU. In the end, within the terms that the Swiss government is obliged to act on a federal referendum passing, they did the absolute legal minimum to meet the wording of the referendum, annoying the SVP (who sponsored it) and fellow nativists as not being in the "spirit", but opinion polling recently on the matter among Swiss voters now sees the original referendum result as a mistake.
* The legalese that is bundled into formal acts that pass parliament, international agreements etc. demands that the language bound in them are specific to a very high degree lest there are any challenges to them. Back in June 2016 the UK was asked wherever it should withdraw from the European Union - it did not ask the electorate how the UK should then conduct its relationship with the EU after withdrawal. Anyone claiming that "everyone" or at least "nearly everyone" that voted leave knew what they were really voting for beyond what was asked in the referendum question is talking bollocks. That includes Theresa May. Such language and behaviour may be acceptable in the spivs, dodgy businesspeople and conmen and conwomen that dominate the modern Conservative party and the leeches that suck its blood, but in continental Europe that shit tends not to fly too well. Especially in Brussels.
* We'll not even go over several other points that have already been made plenty of times - questions surrounding the activities of prominent "leave" campaigners that are still under investigation by the NCA, attempts by May's government to use Henry VIII powers to bypass parliament until the Supreme Court put a stop to that, the abusing of centuries-old protocols in the House of Commons, the unwillingness of Brexshitters to own their mess and blame everyone else for it etc. etc.
* Finally, democracy is a living thing, and like all living things it evolves. It has not stood still in Ireland since 1922 and it has not stood still in the UK since 2016. People, businesses, authorities etc. can change their minds and local, national and international laws accommodate for this and so they should be. It's one of the reasons why the likes of myself alongside many others are strongly against international trade deals that allow corporations to sue governments because of decisions made by elected administrations on behalf of their electorate could risk such corporations' "future profits", to be decided by a commercial court of arbitration that isn't accountable to the electorate of any country involved. The sad irony is that many of the proponents that talk of leaving the EU to "regain sovereignty" would only be too happy to hand it and more to foreign corporate behemoths. And that includes the charming but vapid & soulless c*nt at the head of it that in his celebration of the 2016 referendum joked about it having been achieved "without a single shot being fired" when a few days prior an MP had been shot dead because of her stance in the said referendum. In many cases that would have had him ostracised from mainstream politics. But we're stuck with a parliament that is either understandably scared for their safety, or is a nasty enough bit of shit themselves to giggle quietly under their breath. Edgy.
Fuck, that's 'nuff for now.