Stan Carey has a mental_floss post on the word Celtic that says just about everything that needs to be said on the subject. He explains that “The now-dominant pronunciation ‘Keltic’ is a modern innovation”:
We can see the shift by comparing Fowler’s original Dictionary of Modern English Usage with Robert Burchfield’s revised third edition. Here’s Fowler, 1926: “The spelling C-, & the pronunciation s-, are the established ones, & no useful purpose seems to be served by the substitution of k-.” Burchfield, 1996: “Except for the football club Celtic (in Glasgow), which is pronounced /’seltɪk/, both Celt and Celtic are pronounced with initial /k/ in standard English.”
Burchfield doesn’t mention the Boston Celtics, and that’s not his only oversimplification. Celtic may be pronounced either way in standard English—even if this bothers some people. A lot of antagonism over language use stems from misconceptions about correctness, such as the common belief that there can be only one correct form of a word (one meaning, spelling, pronunciation, etc.), and that variants are therefore wrong. […]
According to the Merriam-Webster Dictionary of English Usage, “the closer you get to circles substantively concerned with Celtic lore and languages, the more likely you are to hear \’kel-tik\”—though “Seltic” may be heard “at times from very well-educated speakers.” The American Heritage Dictionary elaborates:
Although many people pronounce this word with an initial (s) sound, an initial (k) sound is standard in historical, linguistic, and sociological contexts. Interestingly, the introduction of the (k) sound is a linguistic change started by scholars, contravening the historical development of the word.
English borrowed Celtic in the 17th century from French celtique, soft-c, and from Latin Celtae, also soft-c in Britain at the time (unlike Classical Latin, which used a hard c). Centuries later the pronunciation changed, because language, but it didn’t switch from “Seltic” to “Keltic”—it just added the variant, which then spread. So now we have two acceptable forms. (And two spellings: Keltic, though unusual, is a variant that recalls Greek Keltoi, “the Gauls.”)
As both a Celt and a linguist, Stan is in a good position to adjudicate the matter, and his conclusion is unimpeachable:
Claims about correctness in language can’t override the facts of usage, and the important fact here is that both pronunciations are standard and correct. […] Critics are entitled to dislike “Seltic” or “Keltic,” but they have no business saying either pronunciation is wrong. Because they’re both right.