Today, too many Irish trad players trivialize the use of the word 'Celtic', which, ironically, continues a centuries-old cultural bias (among English and French speakers) that alternatively served (a) to preserve the language while demolishing the political power of indigenous Celtic peoples, e.g. in Brittany which in the late 1600s supported an illiterate (in French), monoglot Breton-speaking enclave, and (b) to eradicate Celtic languages and de-Celticize Celtic lands through displacement of the native population, e.g. across 16th-18th-century Ireland where the gradual extinction of the Gaelic-speaking gentry led to the end of patronage of poets and musicians, and worse, the total demise of classical Gaelic scholarship.
Modern-day Ireland, owing to its enduring Gaelic language culture, is still the Celtic country par excellence (French-English expression) in Europe. In the early sixteenth century, most people "beyond the pale" spoke Irish Gaelic (Gaeilge), a (boring) Q-Celtic language. The 'Pale' was the base of English colonial rule in Ireland during the Middle Ages, a band of land lying between Dublin and Drogheda. The term is still used in contemporary Irish speech, often critically, to refer to County Dublin and nearby counties—e.g., when governmental funding and resources are unfairly concentrated on those within the Pale.
With the conquest of the native Irish who had the most fertile land, knowledge of Irish (Gaeilge) and "Irish ways" was pushed westward, relentlessly, until it was restricted to the poorest people in the most barren lands of the west.
Knowledge of Irish had become synonymous with poverty and illiteracy (as defined by the relatively new English speaking majority). In the sixteenth century, Q-Celtic language had extended from southwest Ireland to northern Scotland. "The decline of classical Irish weakened the literary links between Celtic Ireland and Celtic Scotland, as did the fact that the two countries came to follow two religious paths." Source: John Davies, The Celts (London, UK: 2000), 158-165.
After the devastating Irish famines of the 1840s, that principal sign of Celticity—a people fluent in their own Celtic language—was down to roughly a quarter of the population, and only six of Ireland's counties had Irish speaking majorities.
Fortunately, Irish and Scottish Gaelic speakers, though small minority groups, survive to this day in predominantly English-speaking countries. Manx Gaelic, sadly, has the distinction of being the only European language to become extinct in the twentieth century.
The last native speaker of Manx, Ned Maddrell, whose first language was Manx Gaelic, died on 27 December 1974.
The Manx language has been revived, to a very limited extent, among Celtic scholars, Manx choirs, folk singers, and in the Manx educational system. But it's still a revival of a broken native tradition. The very same could happen to Irish and Scottish Gaelic, as has already happened with Cornish (a P-Celtic language), which went to its death even while other P-Celtic languages (Welsh and Breton) grew in terms of the number of their speakers. Another P-Celtic language, Cumbric, closely related to Welsh, has been extinct for centuries.
A lot of people don't know it, but the Bee Gees (the three Gibb brothers) were born in the Isle of Man—not England, not Australia—and regularly paid tribute to Manx traditional culture, recording and performing 'Ellan Vannin' at their concerts worldwide. (It matters not that they were born to English parents.)
The term 'Celtic' is used freely by linguists, historians, artists, music historians, folklorists and musicologists in the contexts of language, culture, music and dance—all living traditions that exhibit 'Celticity'. Historically speaking, not even an awareness of kinship to other Celtic tribes, or similar tragic colonial experiences, or the irretrievable loss of communities, could bring about a sense of a common 'Celtic' ethnic identity.
This is true for all six Celtic nations, not just for the Irish.
So what does Celticity meanfor English speakers?
Celticity maybe has everything to do with language families (P- and Q-Celtic) and the Celtic peoples who speak (or once spoke) them in Wales, Brittany, Cornwall (P-Celtic); Ireland, Scotland and the Isle of Man (Q-Celtic), also in ex-Celtic lands and in the Celtic Diaspora.
I am not conversant in Irish, though I have a few choice words and haven't given up on the prospect.
My own use of the revivalist term 'Celtic' is mainly to describe tunes that originate or derive from the music of the six Celtic nations, also ex-Celtic lands, and the Celtic diaspora. The panceltic.ie/ ">Pan Celtic Festival in Killarney, Ireland has bands from all six Celtic nations competing annually for top honors. Its aim is to promote the modern Celtic languages and cultures and artists from all six Celtic nations: Brittany, Cornwall, Ireland, Isle of Man, Scotland and Wales.
In my Mel Bay books and BHO blogs, I have laid bare the playing and ornamental techniques that comprise Irish and Celtic fingerstyle banjo, which can be used to play music from all Celtic traditions, which are not one and the same.