Keltic vs. Seltic: always a hard call. Our usage of the word "Celtic" comes to us from the ancient Greek "Keltos/oi" and as a direct borrowing from the Greek would warrant the hard c = k. The Roman/Latin c was also hard (in other words, they used c when transliterating the Greek kappa, and s when transliterating the Greek sigma). However, we have brought the term into English, in which the c followed by the vowel e softens into c = s. People who study Celts for a living split on the issue. One of my profs -- herself of Celtic descent -- used to insist that she would violate English usage and pronounce Celtic as Keltic only if we would also agree to refer to Keltic kivilization rather than Celtic civilization. Others -- including most scholars of Celtic studies in the US today -- preferred the consistency with the ancient Greek usage and were happier with inconsistencies in English. That's the crowd that would insist that they were from Boston, of Celtic/Keltic descent, and since they were from Boston, always rooted for the Celtics/Seltics in basketball.

Is the use of the term in gaelic with the soft c, to which your duo refers, a usage based on direct lineage from antiquity, or is it a borrowing in Europe/the Brit Isles of the Greek/Latin term? I don't know of any evidence to suggest that ancient Celtic Europeans thought of themselves in anything except tribal terms (as Boii, Tolistoagii, Trocmi, Aedui, ec.), much in the same way American Indians didn't really identify themselves as Indians until the Europeans provided them with that collective identity.