Gosh, that's a hard one to answer but I'll do my best.
First of all I would say that there are possibly a mixture of opinions on both sides of the border. Politics and religion are definitely at play when it come to football as there are two separate associations, although that wouldn't be the case for rugby for example which is an all-island sport with a United Irish team playing together.
I would also suggest that a majority of (not all) Nationalists in N.I. would support the Republic rather than the North as players from Nationalist areas like Shane Duffy and James McClean have chosen to represent the Republic after they played underage football for the North. Under the terms of the Good Friday agreement, they have the right to consider themselves either Irish or British and choose a passport from either country. These type of defections have certainly created resentment from some North of the Border. On the other hand, players like Neil Lennon who is also from a strong Nationalist background chose to play for the North relatively successfully when he played for Leicester. As soon as he joined Celtic, he became public enemy number one and they even had caricatures of him hanging from lamp posts. I realise he can be very gobby so he is partially to blame for the attention he brought onto himself in a small way.
On the Republic side, there would also be an element of people who wouldn't support the North in any shape or form. I would like to think the percentage of people like that is smaller the the same kind of people in the Unionist parts of N.I. Back in the 70's and 80's, I remember there being major trouble when Glasgow Rangers and Linfield came to play matches in Dublin. A lot of lads came from the North to support them and they were met by a very hostile crowd from down here. So, there is/was a small element here who are just as bad as their counterparts from the North.
As there has been relative peace for the last 26 years or so, I would like to think things are a bit different now. Back in 2016 both sides of the island qualified for Euro 2016 in France. I flew out of Dublin Airport to head over and there were huge crowds of lads from both sides drinking in the airport bars. No flags visible but there was a bit of banter between both sets of fans and no hint of any trouble.
Northern Ireland are now playing Slovakia in the play off final in a few weeks. I am sure there will be an element who will be cheering Slovakia but I would like to think, the majority would prefer to see Northern Ireland win. Remember, the winner gets to play Poland and Sweden in two games in Dublin and Spain in Bilbao. The hospitality industry in this city would make far more money if N.I. qualify instead of Slovakia.
I hope that gives you an idea of my own sentiment. It is not straight forward lol.