[User23]

There is no such thing as “celtic” culture. Celtoi is a word of precision roughly on par with “barbarian.”

[NoboruWataya]

Despite the looseness with which the Romans originally used the term, it seems well established that the groups of people who came to be regarded as the "Celts" did have some cultural traits in common: https://en.wikipedia.org/wiki/Celts

Perhaps it is more accurate to say there were Celtic "cultures" rather than a single culture. Regardless, I don't think the etymology of the word itself is determinative.