Reported (so-to-speak) in the Express on 09Jul2016, an Irish political group calling for “Irexit” apparently set itself up. As at 28Aug2016, what’s happened?
Well, not much. http://www.ireexit.com/ reported that “This Domain Name is Suspended” because the registrant failed to validate his/her email address. https://www.facebook.com/irelandexit and https://twitter.com/ireexit seemed to have stopped media feeds on 27Jul2016.
Between 10Jul and 17Jul2016, the public forum http://www.politics.ie/forum/eu/249532-ireland-exit.html sort-of-discussed the matter. The forum reveals a sample of the same strong, emotional polemics that we saw in the British so-called “campaign”. The forum also contains more rational, or at least more structured, thought-processes that we never saw in the mainstream media in Britain, and only occasionally from public comments on newspapers’ websites. One comment on the forum even pointed to the role international law by citing http://www.marinetraffic.com/, by-passing the relevance of the European Union in the process (another comment to http://www.marine.ie/Home/site-area/irelands-marine-resource/real-map-ireland).
There appears to be a greater, more widespread, sense of despair in that public forum about Irish politicians than the British have about theirs (and the British despair is fairly sizeable). One published opinion appears to corroborate the Irish sense, compounding it with a desperate regard to Angela Merkel to run Ireland better than EireGov, expressing fear that Merkel sees the world too black-and-white to understand the Ulster issue.
On balance, I think comparisons between UK and Ireland look way off the mark. Ireland has its own policy choice issues with the European Union, and its own policy choice issues within Ireland. Some of those internal issues have parallels with the UK, but only in principle (“Oh yes, we have that sort of elitist-mafia-hates-the-plebs thing, too”). The scale and depth of those internal issues are substantially different (“Oh, but our mafia doesn’t quite do that...” or “Oh, our mafia does it in a completely different way...”).
Otherwise, I can’t find published evidence from 01Aug2016 to suggest that Irexit is even on the political agenda.