"Which "people involved" would that be; those selected by British politicians 88 years ago, thus creating the present mess, or all the people in involved - namely the whole population of Ireland?"

Hasn't there already been referendums? Both a majority in the Republic of Ireland and in Northern Ireland said that whether Northern Ireland remains within the UK or not is up to the people of Northern Ireland alone. The British people (British as in from GB rather than the UK) had no say in the matter though various polls have showed that the British people as a whole are more in favour of a united Ireland than the Irish as whole are. As to the creation of a united Ireland then I take it that is up to the Irish both north and south.

I take it that Republicans in the north aren't currently really pushing for a referendum as to whether they should leave the UK because they know they suspect they would lose any referendum. Losing any such rferendum would probably kill the debate for a generation at least. It was almost a quarter of a century before a second Scottish devolution referendum. It makes sense that after more years of power sharing and being further away from the violence then unionist opposition may well soften.