Fine Gael are the descendants of the pro-Treaty side, they are the "Irish traitors" told to take down the flag (the Tricolour) in the song as they are accused by Republicans of betraying what the flag stands for. It is a very powerful and visceral song that gets to the heart of the bitterness of the Civil War.Are they the Anti Treaty party?
Fine Gael of course would utterly reject the label of traitors and insist that they in fact have always been the party most loyal to the Irish state and indeed it was they who eventually declared the Republic in 1949, something that even Dev shied away from.
So for a Fine Gael politician to ask, even in the 2000s, for the Irish flag to be taken down as she didn't want it flying at her daughter's wedding might appear to some people as a little bit tone deaf.
ETA: A link to a decent version of the song with a bit of a tongue-in-cheek intro from The Dubliners