Taht's pretty much my goal for the december faction update. This update will consist (unless I decide to change something) from a faction overview screen, where you can see your faction relationship and rank. The initial release will have some simple activity you can do to raise your relationship. Church faction will ask you light up candles near shrines, kobolds will want some meat and random materials and militia will ask you to patrol around the village, which will simply advance time by half a day with a random chance to stumble into some trouble.
Once you do these things enough times and raise your faction relationship, there will be some kind of event / quest you have to complete. This will increase your rank which will give you more money and new activities to raise your relationship.
I will also "add" one unjoinable faction, wild mutants. This is pretty much already in the game in a form of wild kobolds attacking you and more spawning around the island if you keep killing them. I will simply tweak this system a bit and add some cutscenes and more mutant types coming after you together with a way to make them happy so they stop showing up in large numbers.
Those are my plans for the initial version of the faction system. Will serve as a good base for the future updates as I make the island bigger and add more factions.