As the many responses show, there are two ways to pronounce the word. Having said this I do not have an accepted rule with which you can determine when to use "K" Celtic and when to use "S" Celtic. Every one of my Irish friends (both Irish speakers and non) use "S" Celtic for the football team and "K" Celtic for everything else. So the closest I can come to a rule is that if it is a sports team's name it is pronounced with a soft c. If it is everything else (inlcuding music and art) it is with a hard c.

I, too, took Irish language classes and my teacher also told me there were no soft c's in the language. It is true, however, that pronunciation varies wildly from region to region on the island, but I have never heard any Irish Gaelic speaker say anything but "K" Celtic unless they are rooting for the green and white boys on the pitch.