For the rest of the world they will have the same problem as the Americans except they know the word from the football club Celtic which is pronounced with a soft c as well.

And others still will not have heard of either and would think the clubs are pronounced like the historic culture

Why should the people know how the culture is pronounced in English?! (If they knew about the culture in the first place)

As far as I know this is not obscure knowledge (where I am from)

Non-anglo celt here. Selt. Didn't know it's supposed to be pronounced kelt in english (us an uk alike). I upvote GP.

It’s not an Anglo thing. It’s from the Greek name for the people, Κελτοί. That’s a kappa, hard K.

The correct pronunciation depends on language (German vs. Deutsch, for an extreme example), so non-English speakers could still use the wrong pronunciation when speaking English. In my own language, 'celts' sounds like 'kelts', but until now I thought the correct way to say it in English was 'selts'.

This exactly. In French we use a soft “c” and I assumed English did the same because the only use I knew was about Larry Bird's team!