Strictly, on NI:
It has never been part of the Republic of Ireland.
And the Good Friday agreement does not allow for a referendum "at any time". Only when there is a likely majority in favour of the two irelands uniting. I still think that prospect is some way off.
Nonetheless, there is absolutely no doubt that Brexit, both the prospect and the reality, has been a hugely destabilising influence on the whole of ireland and consequently, like it or not, on the union of Great Britain and N Ireland.