A hibernophile is a person who is fond of Irish culture, Irish language(s), or Ireland. Although I can't find a direct source for this definition besides Wikipedia, the Oxford English Dictionary lists its antonym, "hibernophobia". Its root is Hibernia, the Latin name for Ireland.
Similarly terms include scotophile for Scotland and cambrophile for Wales. Wikipedia also has a list of common -phil- terms in this same vein.
As far as I can tell, there is no official word to describe affinity for Celtic cultures, although I see the term "celtophile" used informally.