hmmm, just found this little piece:
"The British Open, Golf's oldest national championship was played for the
first time in October of 1860, when eight men played three rounds over the
12-hole course at the Prestwick Golf Club in Scotland. The next
year, the British Open event was declared "open to the whole world," and the
event has been known simply as the Open Championship ever since."
i never knew that it had ever been called the british open... that more or less settles it for me, then... the republic of ireland is out of contention
Depends on what the word "British" referred to. The Republic is located in the British Isles but is not part of Great Britain (and certainly isn't part of the United Kingdom 
).
It's called the British Isles mainly by the British, but also abroad. The Irish government has been asking cartographers and other governments to stop including Ireland in the term British Isles. Just like Zimbabwe is no longer called Rhodesia, I suppose.
More confusing geograpical tags, Donegal is in Ulster, but it's not in Northern Ireland. It is the most northerly county on the island, though.
...and, Northern Ireland is not technically in Great Britain, but it is in the United Kingdom. It is part of the United Kingdom of Great Britain and Northern Ireland.
Wheter or not it's likely that the R&A would consider going outside the U.K. for the british open, I don't think it would ever be held in the Republic of Ireland.