Mike Laidlaw and others have said that companions can desert the Inquisitor during the course of the game. Does this stand true for the advisors as well?
I'm curious how they will respod to orders which conflict with their principles. Leliana is tasked with carrying out covert operations and assassinations. If you ask her to murder-knife a member of the Chantry, is she going to pack up and leave?
Great overall question. Given that the interview about Leliana seems to suggest that she may disagree with Cassandra on some issues, I get the feeling she might have an idea on what direction the Inquisition should be headed, and it's possible the Inquisitor can take it on a path she may dislike. Given what she has done in service to Divine Justinia V (given "Faith" and "The Masked Empire"), I'm not too sure where her moral boundaries are now.
Simillarly, Cullen oversees all things military. If you resolve the mage-templar conflict in favor of the former, does that suddenly leave you without a general? (I imagine he would take umbrage with the PC furthering the interests of magic users).
I've wondered how Cullen would respond to a non-Andrastian protagonist, given what he said to Oghren and about the Qunari, and what his current views are on magic and mages. He may have changed considerably since Meredith's fall, but it's not implausible he might have a problem with the Inquisition going in directions that run contrary to what he believed as a templar, and his Andrastian beliefs.
Unless the advisers can be replaced, I'm not too sure they would leave, however.