Traditional Irish Music
As I dislike Punk and Indie music, I slightly agree with your point. However, many real Irish people - those of us who actually live in Ireland, not places like London - would disagree with you. I happen to love the music of the great Donegal band, Clannad - arguably the most successful Irish band in history. Clannad's music falls into your category "modern folk music" and some of their music contains elements of Jazz. Irish traditions are changing and evolving and they always have.
Greetings from Seamus to the Professor