You need to have 100% relationships with the following people to get rep missions unlocked. Note: Make sure to collect piles of trash while they are still around. This is one of the requirements in the Artsies missions. They will disappear after awhile; act fast and do not recycle them until after unlocking the Artsies missions.

Luther Bigbucks: Richies mission.
Darius: Streeties mission.
Polly Nomial: Nerdies mission.
Roxanna Marie: Artsies mission.