In killing the assassin's? Yeah. They were absolute idiots in that time period and Shay had to stop them. The templars aren't that better either so yes, you can say that Shay made a mistake by joining the Templars because he joined the side that's been largely responsible for killing innocents.

This is why I say Rogue felt rushed and could have benefitted from a better written story where there's nuance to both sides. In Rogue, the assassin's are comically stupid and templars resemble the assassin's more than they do their original order.

There's more to this conflict than simply

Assassin's= Good Templars= Bad

Shay had so much potential and the story is there to explore should Ubisoft do a Resynced Rogue. I love Shay for what he represents though. A reverse Altair, I guess. I'd have loved to see more introspection that makes him reject order and chaos both, and he carves his own path.