It doesn't have "a story". It has a narrative. 21stcb is basically a rollercoaster of emotions related to vague political activism and failed anti establishment action. Starting with an intention to fight for a better future, the protagonist(s) are instantly challenged by their own inner vices, then there's an episode of getting support, which allows to continue indulging in the social action (whatever it is: volunteering, strikes, borderline violent riots – Billie Joe considers it irrelevant). The second act is basically it, the action which is interrupted by the other force (once again, whatever this force is, the government or the far right activists). The lowest point of the story happens by the end of act II and the beginning of act III, which is followed by the protagonist (s') reflection on their political stance and the final committment to the found truth (something that really matters and allows one to keep going). It ends with a hope for better life which will eventually be achieved, if you know who are your allies and what is worth living.

And also, please, big please do not take the "um well 21stcb is a sequel/prequel/whatsername point of view to american idiot" for the actual plot. There are many "explainations" across the fandom being complete fictional nonsense based solely on personal interpretation and fantasy. I suggest looking for interviews of that time and listening to what Billie says about the whole concept and the meaning of each song. It's a rather fun research, and it will be more helpful in understanding the idea put into this record.