The False Idols may force all players to redraw their roles, however, if they are called out as a bluff they are eliminated anyway.
Interpreting the False Idols:
The False Idols represent something misleading, whether that be a person or a personal goal.
If The Last President faces you, this misleading entity is probably already in your life, but if Cain faces you, this entity may come into your life or otherwise reveal itself soon.