Whether gayans should or should not be considered Bretonian patriots/citizens depends solely on the militancy of their members; whether as a collective they find foreign occupation more environment-friendly than the current Bretonian rule.
In my op, once the treehuggers started carrying guns and shooting government representatives, they quite automatically made the decision for the whole movement. There didn't need to be a formal renouncement of citizenship because UNLESS an amnesty is issued, gayans are terrorists according to bretonian law and therefore (correct me if I am wrong) each police or armed forces fellow has standing orders to capture them to put on trial and sentence to death by some environment-friendly rope (lead poisoning is a big-no-no) or if that proves impossible due to "resiting arrest" - just blast him outta the stars and fill in a report afterwards. Case closed.
If you ask me, the only way for it to make any sense at all, that Gayans legitimately fight on the Bretonian side against "foreign" invaders is the queen's government issuing an amnesty - "charges dropped if you abandon the movement. You may bring your rag-tag ship, but that's not necessary". But then they don't fight as Gayans - they fight as ex-criminals who saw the light.
And how does this actually work ingame?
Some random NLH and BPA fight in Leeds, then some KNF indie shows up. Bretonians both turn around to smash the weaboo, after he's dead they either continue the duel or part ways on an "I'll get you yet!" basis.