The technical definition of Celtic / Celticity that is broadly accepted by academics and other experts is:
"[A] proven affiliation with the Celtic languages or (for non-linguistic evidence) a demonstrable close connection with them". This definition is provided by Barry Cunliffe, perhaps the world's most respected Celtic archaeologist and Celtic culture expert (Cunliffe and Koch, 2010).
Raimund Karl (2010), a prominent Celticist, agrees with the following definition of who is a Celt:
"[A] Celt is someone who either speaks a Celtic language or produces or uses Celtic art or material culture or has been referred to as one in historical records or has identified himself or been identified by others as such &c.".
Personally, I fully accept the first definition and the second only partially. I would not count self-identification. To this I would add: a significantly long Celtic history (say, at minimum, 500 years), evidenced by language, material culture and some form of association with Celtic "folkways" - Celtic spirituality, consciousness, and the like.
Population groups that have retained a Celtic language and / or material culture (practiced in some regular and meaningful manner) and various Celtic "folkways" combined with a long history of Celticity can certainly be classified as Celtic.
In my opinion, these population groups today can be found only in the Atlantic Facade.