I believe what happened is, at some point in the past we used the soft-c (I guess this is when all the sports teams were named). But more recently it was switched to hard-c, to reflect the Greek origin of the word.

I think that’s right: from 300 AD to 1700, nobody used the word. Medieval Latin dominated in the meantime, and so preferred a soft c in Celtae without an academic to insist on the k in Keltoi.

English doesn't share the same linguistic root, so these differences are bound to appear. Well, if you take out indo-european that is.

> English doesn't share the same linguistic root. […] Well, if you take out indo-european that is.

It's a bit more complex, English is half a Germanic language but also half French.

But that doesn't explains why “Celtic” is pronounced differently in “Boston Celtics”.

That I presume is just the natural evolution of language, their origins fade away, they become culturally assimilated, and pronounced more in line with the hosts. Nothing new. But interesting nonetheless. I don't have a definitive answer but I presume it was something like that.