The Molly political interests for an Independence Party would be very well in line with their RP as the Mollys are terrorists fighting to claim what, they, believe to be theirs. While most Mollys players play purely from a lets-pirate-people standpoint with hints of "Dublin's ours, yeeeah!" the Mollys aren't pirates by choice, that's what they do on the side in order to survive and get revenge on BMM. The Mollys are freedom fighters (i.e terrorists by goverment standards) who have a cause they're fighting for, not just for their personnel profit as then generic pirate would. As such they are quite likely to gain political sympathizers who likewise believe in their cause.
The 'IRA' mentality is something that is actually downplayed more by the Molly factions then what it was originally. The original freelancer rumors and news make frequent references to a Molly plot to steal MOX or other toxic material and detonate a bomb in the atmosphere of New London, poisoning the planet. There's also mention of an assassination of a BMM Executive by Mollys, who was killed by a pick axe. The Molly's "Infamous and gruesome calling card", a piece of fools gold that was left at the scene, suggests that this isn't an isolated incident.
Just like the Gaians are not your average pirate causing trouble, who's cause for a environmentally secure universe being expressed through the the Green Party, the Molly cause for a free Dublin is expressed through the Independence party. As Jammi said the ethic part for political parties shouldn't be relevant.
Although the original freelancer rumors, news and character's frequently reference Irish names, as well as several other hints to the area such as having them fight over 'Dublin'. The Discovery factions have merely extended that foundation in order to enhance their unique brand of RP. While I doubt the entire Irish culture survives if they were separated from the rest of the Bretonian population by social constraints then it might not have been corrupted to the same extent. Regardless the Irish background is something that is now very heavily integrated into the Molly lore by years of faction effort, much like most of Discovery's factions. The accent makes the Mollys one of the more different factions, and far more fun to type out.