We've had to choose between the two sides in all three games and the large majority of players choose mages without thinking twice.
And why wouldn't they? One's first instinct is to help the oppressed. But if it is to be presented as a choice, it shouldn't be so black and white.
While there are a few reasons to be pro Circle and respect the templars' real purpose, the games failed to provide one that is just as compelling as the noble cause of mage freedom.
Which side I choose often depends on the character I am playing and how they would view the issue. Personally, I am a pro-Circle person. Yes, it's not right how mages are simply locked away simply for being born with abilities others do not have, but without proper training, that power can destroy them and many innocents around them. The missions of Redcliff in DA:O is evidence of this. Then there are the fearful masses that would just as soon behead a mage as allow one to live in their town. As Irving said, "The towers walls protect us as much as they protect others from us."
The Gallows was different. Everything that could go wrong, did go wrong in that Circle. I blame that entirely on Orsino. He was a weak, horrible First Enchanter. If he had done his job the way Irving did, things would never had escalated the way they did. Meredith may have used some extreme measures, but what choice did Orsino leave her? From the first act we see blood mages and demons pouring out of the Circle. For a circle to run properly, the Knight Commander and First Enchanter must cooperate. Otherwise the Circle cannot function and will fail and the mages are the ones who suffer for it.
In DA:I, the choice between the Mage arc and the Templar arc is less about the two factions and more about which would be more effective at helping to seal the giant hole in the sky. For this purpose, the mages make more sense to me, though the Templar side is a much more interesting arc, IMO. But there is also the Tervinter involvement to consider. Do you really want to leave those mages, who are not technically part of the rebellion, at the mercy of an obviously corrupt magister? Never mind Cory's connection to what's happening in Redcliff.
Besides, I would much rather those mages be where I can see them and convert a part of Skyhold into a mini-Circle. My Inquisitor would have to be a blindly devote Andrastian, which I have played a couple of those, to go for the Templars. The Circle is not perfect by any means, but it's the least crappy of the available options when it comes to how society deals with magic.