Here are some interesting quotes from a BBC Site which explored the 'Shared Tradition' concept.
The Overview
The Two Nations theory that there are two distinct races and therefore cultures on the island of Ireland, the Protestant planter and the Catholic gael, is very difficult to sustain.
The Song Tradition
When we come to study songs the situation is somewhat problematic. The differences between Orange (or Ulsterman or Protestant or whatever other, sometimes pejorative, shorthand term you wish to use) and green (or Irishman or Taig or Catholic or whatever) song are more apparent than real. Even a cursory glance will show obvious and interesting similarities.
Brian Mullan
The Orange Tradition
So Orange music is really as Irish as anything else on this island, whatever that means, and possibly much more Irish than much of the stuff now peddled as being Irish. Two hundred years ago there was no other kind of music in this country than traditional music, at least as far as the ordinary people of either religion were concerned. The fifing and Lambeg tradition, perceived as an Orange, unionist thing, also existed on both sides of the divide at one time, with a common musical collection of tunes. The whole musical tradition associated with the Orange Order has its roots squarely in the dance and song traditions as well as the military traditions of Ireland, Scotland and England. But it is still part of Ireland's musical tradition.