Well, Northern Ireland isn't the Republic of Ireland, otherwise it'd be called the Republic of Ireland. It exists because of the pro-unionists in that area of Ireland that wished to remain part of the UK.
The simple fact is that at this present time, the majority of people in Northern Ireland wish to remain in the UK. The whole point of the Good Friday agreement was that the dispute as to whether Northern Ireland should become part of the Republic of Ireland, or remain as part of the UK should be settled via political means rather than via terrorism. Yes, it's a thorny issue to many, but disputes should be settled peacefully and via democratic means.
Territorially, it's a similar situation to Scotland. Yes, it has its own devolved powers, its own parliament, and a political party that would wish to see it separate from the UK. But from a democratic perspective, Sinn Fein have been unable to secure a Northern Irish majority that would allow them to call a referendum on seceding from the UK.
If anything, Scotland has become closer to leaving the UK due to the SNP having a majority in Scotland and holding that referendum on leaving the UK. However in that instance, the voters decided they'd prefer to remain part of the UK. It's the people of Scotland that have to make that choice, not the choice of the rest of the UK. In much the same way that it's the opinion of the people of Northern Ireland that matters the most regarding their future, not the opinion of those from the ROI.
Hence for NI, until the populace votes in favour of a party that wishes to leave the UK (and merge with the ROI), and then the populace votes in favour of leaving the UK at a referendum, they are part of the UK by choice. And at the end of the day, choice of the population is what matters.
And as long as NI wishes to remain part of the UK, the details of the Good Friday agreement that settled those tensions (to a degree) and provided peace to Northern Ireland are very important to observe. And of course, Brexit threatens those details.
EDITED: 18 Dec 2017 22:24 by DAVE!!