By no means are all songs about Irish factions rebel songs! There are many, many loyal songs, or Orange songs. Indeed, there are books on the subject:

- Neil Graham's The Orange Songster
- The Orange Lark

I don't have a keyword for Orange songs in the Ballad Index (a regrettable mistake), so I can't pull a complete list, but some that spring to mind are

Derry Walls Away
A Loyal Song Against Home Rule
No Surrender (I)
No Surrender (II)

And a whole bunch of Boyne songs.

"Green" songs were certainly more popular than "Orange" songs, but I'm far from certain they were more numerous.

So a faction song might be Green or Orange; it simply took a side on the issue of Irish independence.