Some of those Orange songs are beautiful. If you're interested in the tradition, you might try Songs of the Ulster Protestant - this is listed as 'various artists' but the artists aren't named on the Amazon listing, unfortunately.

A lot of the songs have that wry humour that's typical of Northerners of both traditions, like The Auld Orange Flute, which tells of a loyal flute whose player converted and attempted to bring it with him; it ended up being burned at the stake while still bravely playing - what else - The Protestant Boys.