Hmmm... specifically (Southern) Irish... off the top of my head I can only think of battles they're fighting with each other . They were quite late within Western Europe to legalize gay civil unions, of course, but even that happened in 2010. Note that nowhere that introduced them (or marriage), even when it was the Left that passed the laws against the Right's opposition and the Right later returned to Government, any but the fringest parts of the Right have shown the slightest interest in turning back the tide.
But just look at the German school system and the battles we're still fighting routinely. Or of course the Spanish Conservatives' attitudes towards the regional nationalisms. Etc.
Ah, ok, I get you now. In Irish context a better example would be attempts to create a land/property tax and stricter zoning restrictions, up until the crisis they had been rather successful (still are on certain issues)
Of course what is unusual about the US right is the extent they have tried to turn back the tide on certain issues (known absurdly "social issues" in the US), which is surely related to the way these debates developed in the 60s and 70s. I think if you compared the US right and the European right in the 60s you would not think there was a huge difference (the Left would be another matter though..)