Maddy and Az
What if your mid-life crisis was that the secret police are after you? This is the situation that Maddy and Az are in. David's parents, they were both doctors in the city. Which means that they both were going along with the system: they were made pretty, they probably did the typical new pretty thing of going to lots of parties and drinking a lot, and the doing the middle pretty thing of getting jobs.
So Maddy and Az are totally typical people. Only we're hoping that maybe they weren't quite as brain damaged as the rest, because, you know, brain damage.
Not So Typical
Working for the city, they discover that the pretty surgery also includes brain lesions for no extra cost (what a deal). And so Maddy and Az do a non-typical thing: they rebel against the city and the pretty system after they've been working for it for a long time. Do they feel guilty about that? It's not entirely clear since they never really mention their work supporting the system. But they are working against the system now, so it's clear that they think the system is wrong.
Because of that, Maddy and Az serve mainly as information sources in this book (as well as a source of tea): they give Tally the information that changes her view of the pretty surgery. As Maddy tells Tally, the brain lesions only appear in pretties, but some pretties are lesion-free:
In some pretties, they disappear, or are intentionally cured—in those whose professions require them to react quickly, like working in an emergency room, or putting out a fire. (31.34)
From that, we learn that the brain lesions aren't just a side effect: they're purposeful. And this info about the brain lesions completely turns Tally into a rebel. They also clue her into a totally new view of the world: maybe everything is peaceful now because people are brain damaged: all they have now is "Just masses of smiling pretties, and a few people left to run things" (31.56).
Finally, after Az dies, Maddy gives Tally a way to redeem herself. That is, Tally wants to fix the mess she caused, and Maddy helps her out: she can be patient zero for experimental cure. (Try an experimental cure? Sure! Tally's a risk-taker, after all.)