Celtic is a linguistic term, so it makes sense to talk about a language as being Celtic, or having some Celtic words. But once you start using it as a term referring to some notion of race or nationality, it's really a misuse of the word. And it leads into all kinds of dark places.

It's the same with other language words, like "semitic", which are misused as racial labels.

So Irish is a Celtic language, and the English spoken in Irekland has many echoes and traces of Irish. And a high proportion of the ancestors of most Irish people used to speak Irish, or Scots Gaelic. But there are also ancestors from all over the place. And the people in the Galeltacht have ancestors from Norway and other places as well. And the music played in Ireland has echoes of the music played and sung by all these ancestors, and it is possible to identify some of these echoes, and say where they come from.

But basically when people talk about "Celtic music" referring to what happens in a session, that's nonsense.