(...) and then turning my back on them to side with the Templars and knowing you are slaughtering them.
I might feel differently if I had the chance to talk to the Templars somewhere in a similar fashion and realize that many of them are just as sold out.
Your character doesn't know that their choice at that moment is determining the fate of either faction, though. You, the player, know it because there's a giant red message warning you that working with one side will make it impossible to work with the other. But your character doesn't know that.
With that, if you have Cassandra in your party at the time you meet Fiona, she's the first to suggest that you need the Templars to deal with this. That's actually the way the Champions choice was supposed to play out, if it had been as railroaded as the Whispers choice was: at the point where you meet Alexius, your character makes the choice of either dealing with the situation themselves, or deciding that this is beyond them and getting the Templars to handle it. Either way it goes balls up - but the knowledge that by choosing one side you are dooming the other is metagaming. Your character has no way of knowing that, so it would not even go into their consideration of how to deal with what they've just found.
Re. the chance to talk to the Templars before starting their quest: that's in the first time you go to Val Royeaux. You see Lucius, he makes an outrageous speech that raises a thousand red flags, gets his sanity questioned by Friendly Neighborhood Good Guy Ser Barris, and then again by Cassandra. All the plot signals that there is something very wrong with the Templars are in that scene. Perhaps because it's too early in the game some people have forgotten about it by the time they get to Redcliffe? But you do get the same forewarning for both sides.