Without turning this into a flame war...
What exactly has Subwoof done so bad that they can't compete in the campaign?
All they really have to do is turn up to a match and compete. If they wanna troll or stir people outside of the campaign, then that's their own business.
According to Juleh one third of Subwoof have received bans on GON servers. ACC1 is a GON admin, and he's also the sole person organising/running this campaign. This campaign is virtually a 'GON campaign'; so behaviour on GON pubs is going to affect your chances of playing in the GON campaign.
Analogy: ACC1 owns a pub. Subwoof come to the pub and 33% of them start fights and break chairs over patron's heads. ACC1 kicks them out.
Next week, ACC1 announces he's starting a wet t-shirt contest, Subwoof_ say 'hey can we come spectate?', ACC1 says 'no, the Subwoof_ name is tarnished in this pub'. Subwoof say 'that's BS someone else should run this pub'.
Now you guys might go and dispute little details here and there, I don't mind, remember KoS in general have no say on Subwoofs participation (I helped you guys try to get in), I'm just attempting to explain things from ACC1s perspective.
TL:DR - "If they wanna troll or stir people outside of the campaign, then that's their own business."
- this is having your cake and eating it too
Plus how am I meant to fight in the campaign?
Just like anyone else; pick a team and sign up. You could argue that because the rules never mention the word 'clan' that you simply fight for a side as a permanent mercenary.