The rap trio said the case is politically driven, and that the Crown Prosecution Service has submitted nothing new in its appeal.
The 27-year-old rapper was accused of displaying a flag in support of proscribed terrorist organisation Hezbollah at a gig in November last year, until a technical error in the way he was charged led to the chief magistrate ruling he could not try the case.
The Crown Prosecution Service said in a short statement it would be appealing against the decision because "we believe there is an important point of law which needs to be clarified".
The trio expressed outrage over the appeal decision on social media.
"Once again this is a massive waste of taxpayers money, of police time, of court time," they said on Facebook.
"We will fight you in your court again. We will win again."
The rappers said there was no "important point of law" and said prosecutors had not submitted nothing new in their appeal.
"What there is though, is a state wide witch-hunt against Palestinian solidarity," the band said.
"The media were gleefully informed about this appeal before we were."
The decision to appeal against the judgement comes as Attorney General Lord Hermer warned shadow justice secretary Robert Jenrick not to prejudice future proceedings against O hAnnaidh, asking him to "carefully consider any further public comments".
Jenrick had previously written to Hermer calling for an urgent inquiry into the issue, claiming it "raised serious questions about the competence of all those involved".
Prosecutors allege O hAnnaidh can be seen in a recording of a gig at the O2 Forum in Kentish Town, north London, which shows him wearing and displaying the flag of Hezbollah while saying "up Hamas, up Hezbollah".
