Even though we know hardly anything about the Post -apocalyptic version of Europe in general its still fun to speculate.
Now before we get started i'd appreciate no stereotypes be mentioned.
In my opinion like in real world Ireland most likely opted to remain neutral during the rescource wars, but collapsed like its neighbours. even if neutral
i'd doubt the Republic of Ireland would be a target during the great war, but Northern Ireland most likely was because in Fallout's alternate timeline i think its said that Great Britain still included Northern Ireland up until the great war. However if Northern Ireland was nuked the resulting radiation would affect the many rivers and would irradiate and mess up all of Irelands water Supply and even if Ireland wasn't attacked at all. Britain getting mass nuked would effect it anyway with the irradiated Irish sea flowing into Irish rivers.
In Terms of Post-war Society, The Irish most likely collapsed back into ancient like Kingdoms each led by a differen't king and i would like to think a high king is vying for control of the Island, . Raiders with Celtic influence would be rampant. Mutated irish fauna, Radhares, Raddeers
Radseals etc, Various mutants based on Creatures from Irish mythology. Anyway thats my theory.