Factions play a large role in sheltered 2, and were not an element of the initial game at all.
Each faction has multiple different kinds of "jobs" that can be accepted (once accepted, they can never be quit). Two jobs are available for each faction at first, and getting to 200 rep with that faction unlocks a slot for a third job. Jobs seem to refresh a few days after being completed.
- Give items: Collecting an assortment of random items and then turning them over to the faction (they will send someone to collect them).
- Find a "rare item:" A MacGuffin item will be placed in a random location nearby. Searching the location will find the item; return it to your base and call the faction to come collect it.
- Rescue a hostage: A location will be highlighted on your map. Interact with it to trigger a battle with one member of the faction that owns that territory. The battle is particularly easy but triggering it will lose 50 points (sometimes more - maybe a bug?) with that faction, even if you knock out the attacker without killing them. After the battle, simply contact the faction again to complete the quest. Note: this is the only job that requires losing rep with another faction, but the rep loss is 50 while the rep gain for completing the job can be much higher (depending on your faction goals progress) so the result is a net gain.
- Capture a faction member: You will need a prison for this quest. Find and capture a member of the requested faction by knocking them out and sending them to prison. Contact the faction and they will show up and retrieve the prisoner. Note: if you have the Charisma skill to avoid random encounters on all your faction members, this job will also require losing rep with another faction because you'll need to actively attack them.
There are six starting factions.
Defeating or allying with all factions starts the option for the End Game. (Warning: spoilers)