The "most correct" pronounciation in terms of contemporary usage is the hard C, with the exception of two professional sports teams, the Boston Celtics (soft c) and the Glasgow Celtics. Contrary to Martin Ryan, I've never encountered anyone in Ireland using the soft C. The words Celt and Celtic are always pronounced with the hard C. The pronounciation of those words is never an issue in Ireland really, unless it is to point out the cases of the sports teams mentioned above comes up. Then, it is usually agreed by everyone involved that it is the sports teams use an improper/wrong pronounciation. I don't think it is any different in Scotland.

Historic usage, as someone has pointed out, is fraught with complexities one is better off ignoring completely, if all you want to know is how to pronouce the words "Celt" and "Celtic" without sounding ignorant.