Is it possible to join a different secret society?

Can you change your faction without rerolling your character? How?

If so, can you access faction-exclusive cutscenes for content you've missed? (The only real compelling reason to change factions short of PvP, I suppose).

Solution 1:

No; you have to reroll to join another faction

The secret societies are factions that players can join. United by a common goal to battle evil, they are nonetheless in conflict with each other in the pursuit of power. In the player-vs-player aspect of the game, they will compete with each other for resources, territory and world domination. Once you join a society, you are stuck with it for life.

Source: http://pc.ign.com/articles/102/1023335p1.html

It will be impossible to change factions without creating a new character.

Source: http://en.wikipedia.org/wiki/The_Secret_World