Far too much attention has been paid to this issue, for example from The Sun:
The issue of the border between Northern Ireland and the Republic has been a stumbling block to Brexit talks
The whole thing is nuts. The underlying logic is that any country with a land border with an EU Member State must also be or become an EU Member State to avoid the 'hard border' issue.
I don't see why the Irish-Irish border is of any more significance that the Swedish-Norwegian border, or the German-, Austrian-, Italian- and French-Swiss borders.
Put it another way, just imagine The Republic of Ireland had only recently become an EU Member State and the UK never had been - whose problem is it to sort it out?