The Irish Republic is not part of UK. The Irish probably are unlikely to easily forget being considered barbarians by the English for hundreds of years.
Based on my few conversations, I would say that the person on the street or running the shop is not particularly happy to be in the EU. They are economically weak. The question they might want to consider is whether they would be better off in the UK. History suggests that neither option is very good.
Actually, Ireland is, and always has been, a dependency of Britain. Britain being in the EU was a godsend, because the agricultural and very close social ties could continue while pretending they didn’t exist at all.