Him turning on Meredith for being completely insane doesn't really tell us much about his opinions because anyone with any sense (and backbone) would have done that. Also him leaving the templars could just be because he does not support separation from the chantry.
He could have the same views as he did in DA2 or worse for all we know, I am not saying he does but I don't think it's entirely unjustified for people to be wary of him.
He's a grey character and I don't think either side is wrong in trusting or not trusting him.
[DA]: Cullen made a pretty big decision at the end of Dragon Age II. How has his life changed since he sided against Knight-Commander Meredith?
[BB]: Meredith was Cullen's commanding officer; he wanted to trust her. But standing against her paved the way for him to help form what would become the Inquisition. The templars failed to protect their charges and the people of Kirkwall. The Order has not lived up to its ideal, and though it wasn't easy for him, Cullen now recognizes that. It's something he's still processing, but he's looking to move forward and fight for something he can believe in. The whole world's falling apart, and Cullen won't sit by and watch that happen. He wants to be part of a solution. If that means serving the Inquisition instead of the Order, then that's what he's going to do.
That doesn't read like he left just because the Templars had a falling out with the Chantry.