Yeah, we don't know that he's not a Templar anymore, really. The only hint we had about that was that one dialogue tree where he says Knight-Captain is not his title anymore.... which it's not, since he's Commander now. Knight-Commander? Maybe just your Commander? But it doesn't mean he doesn't consider himself a Templar anymore, all we know for now is that he has a different title these days.
Since he's still wearing the Sword of Mercy on his gauntlets and a very Templary-robe under his breastplate, it does look like he's still pretty loyal to the Order, just maybe not involved with Lambert's Templars (who also may not necessarily be the same as Red Templars, for all we know about them right now). The whole Order is very fractured since the accord was annuled, there's all sort of Templar branches going different ways. Cullen and his men are probably in the most moderate side, working with everyone to restore some order to the mess.