The Centraurian Supremacists started as a terrorist organization centering in New Mars. They arose after the capital of the Beta Centaurian Empire was destroyed and New Mars declared independence. The group was started by patriots of the empire who had been brain washed to incite violence and murder should Empire fall.
Eventually the group grew in number and after the leader was assassinated the group acknowledged that their past terrorist tactics of harming civilians and causing mass terror was "evil", the group ceased causing terror and began fighting to only topple the government and not kill everyone in the process. Thus they ceased being terrorists.
During this time New Mars was unable to communicate with Centauri Prime after pirates and raiders destroyed communication satellites and New Mars was on the other side of the star for a few years. Therefore the current leader of the New Martian government proposed that because Centauri Prime was unreachable that fighting over New Mars being independent or going back under the Empire was irreverent as there was no Empire to fall under.
After the peace treaty they became a political party instead of a separate group. Part of the treaty stated that when the fate of Centauri Prime could be established, and should the Empire still exist, they would put to a vote whether or not to rejoin. Until then it was a mute point and there was no sense fighting for it.