It then made me wonder to what extent was the Catholic Church losing influence in the RoI, and how such a loss of influence would play out with respect to any unification?
That's an interesting point peregrina and you're by no means the first person to have made it. Though ROI has always been seen to make noises about wanting reunification, at least until GFA, there's long been speculation about how a pretty monocultural state suited a lot of people in ROI rather well. It's less pertinent now there's immigration and the influence of the RC Church is declining. But a few decades back, introducing a bloc of 20% of the population who didn't subscribe to the Catholic Celtic cultural tradition didn't necessarily stand to benefit those who saw themselves as upholders of that tradition.
I know some within Irish Republicanism have always taken the view that they could get those silly Prods to come to their senses, but not all by any means. Some always saw that they were more likely to preserve the preferred cultural hegemony by not diluting it.
It is not the case that there is universal support for a united Ireland among the Catholic population (about 45% of the total) within Northern Ireland and I am unclear as to why Brexit should change this.
As was explained upthread, a significant minority of Catholics (and some Protestants) oppose reunification not on principle, but because they consider the UK to be a better gig than ROI. Basically they're fine with the status quo provided the status quo does its part of the deal, and leaves them better off. Which it always has since GFA. There was a brief period in the 00s where ROIs income per head was higher than the UKs, but it didn't last nearly long enough to make an impact. But Brexit clearly has the potential to at least make people think this won't continue to be the case.
Even if we were to somehow escape a recession, and I think most sensible Brexiters concede there'll be at least something as we get through the uncertain stage even if they think we'll be better off eventually, the fact that some people are worried about one coupled with worries about a hard border clearly has the potential to erode this conditional, pragmatic support for remaining in the UK.