I think Cullen will feel like the rug's been pulled out from beneath him when the Nevarran Accord is broken and the war begins. At the end of Act 3, ca. 9:37, he finally starts to think for himself and decides what he truly believes the Order stands for, which is notably different from Meredith's view. I imagine him believing in some absolute golden idea of what the Order stands for, enshrined in the glittering spire in Val Royeaux where the Knights-Divine oversee all that is good and just in templar land. And, then suddenly that all changes, and it's Meredith and crisis of faith all over again. Does he follow the new direction of the Templar Order, or what he believes the Order stands for? I bet it will be very difficult for him... no matter what he's doing once 9:40 rolls around.
Which side would he choose? Hmm, I see him believing that the templar's role continues to be that of guardian instead of hunter, that mages shouldn't be out and free in the world, but that it's not his job to hunt and kill them all. I also see him being quite devout and having trouble with the Order divorcing itself from the Chantry. So, if he's still a templar at that time, I could see him staying loyal to the Chantry. If not... well, I have all sorts of scenarios brewing in my head!