Your followers’ faith in your cult drives everything in Cult of the Lamb. If you fail to keep them fed and happy, or if you decline their sub-quests too much, or even simply neglect to clean up their poop, their faith will drop. Any kind of wrongdoing, neglect, or slight against them, can cause them to lose faith in you. This will be stressful but don’t fret too much over it. In my 19-hour playtime, my cult’s faith hit basically zero multiple times, and I usually only lost a follower or two (they’d steal 10 coins and peace out).
When faith first reached zero, I was terrified – I assumed that’d mean game over, or I’d lose a bunch of my followers, but that’s not what happened. If you run out or have little faith, just focus on getting it back up, and you’ll be okay. Of course, I don’t recommend letting it sit there for a while, but your cult will be alright if it needs to be low for a day or two.