I'm Irish and am a member of the Galician Centre here in Brussels and go to a lot of their weekly concerts of Irish, Scottish, Breton, Manx, Welsh, Galician and "world" music. I certainly think of Galician and Asturian music in the same terms as other "Celtic" music (inverted commas as I don't want to start a hornets' nest about "Celtic"!). The Galicians I know are all very pround of their "Celtic" traditions and heritage as I am of my Irish heritage but they are very respectful of other musical traditions, as I am, and provide a very good platform for these in their Centre. Personally, I don't think of anyone as a "Celt" but as Irish, Scottish, Galician, etc.
Not sure how well this answers your question Adolfo?