It's an acquired taste, certainly. But I (personally) find Chantry-leaning characters very interesting to roleplay, because they become more intriguing, more complex to me. I have a hard time really getting into a mage playthrough because it ends up very simplistic, I fall into this routine of taking the nice guy side every time, freedom or nothing, defending people who really don't deserve defending, etc. With a more pragmatic Chantry-leaning character, I have to question their motivations, think about why they would do this or that, explore paths the game seems to push you away from, always keep reminding myself that people are morally grey and sometimes their decisions are not easily explainable by simplistic black or white views. Siding the with the Templars in Broken Circle, in example, is generally considered the "evil" choice, but even Wynne and Irving themselves agree that annulment is always a tragedy, but in this specific case it was for the best. It's not something I did lightly the first time I tried this path, but my character had (very long thought through) reasons to make this choice, and I was pretty surprised by Wynne and Irving's support. It ended up being my preferred path because of that final revelation of their characters.
In any case, playing Templar side doesn't mean you always support Templars every time, even when they're being awful (like playing mage side doesn't mean you're gonna support the Denerim slaver just because he's a mage). I'm just very skeptical of the whole mage/templar conflict and don't really align with either side (both are dead wrong, tbh), but tend to agree with Templars more often than I do with mages (not on the whole "mages aren't people," or "let's annul this entire Circle who did absolutely nothing because an apostate NOT in this Circle did something," of course), so that's how my characters tend to roll. Obviously there are as many awful Templars as awful mages, rotten apples are everywhere, and those need to be dealt with with extreme prejudice - I imagine when Cullen says "we are not Templars anymore" he's referring to the Red Templars, and how far the order has fallen. I'll gladly slay every Red Templar we meet, for dishonoring the order and the Chantry and basically being blood-thirsty psychopaths.
That's the moderate path my Trevelyan will take - generally Chantry-leaning, conservative regarding Circles (yes for mage rights and even self-moderation, nay for completely unchecked freedom aka Tevinter 2.0), radically against abominations and blood mages, and extremely angry at those rotten apple bastards that now form the Red Templars for twisting and corrupting Andraste's words into a gross power play and pretty much ruining everything. And I think this new, more moderate Cullen we have now will get along with her just fine. (it all turns back to getting dat booty in the end doesn't it
)