There are no purely "Catholic parts" anymore than there are purely "Protestant" areas, so you still end up either displacing people or people ending up in areas they don't want to be in, also just where o you draw the line on this? Carve up Belfast?If Ireland made it clear they only wanted the Catholic parts, would the British public have the political will to support such a war?
Also what if Ireland tries this while the British military is tied down in the Falklands?
As to Falklands era, DF slightly more modern but basically still the same capabilities, British Forces still far too modern/large/supported/capable.