As Captain America: The Winter Soldier established, Project Insight's goal was to identify any threats to HYDRA taking over the world (and they meant ANY threats) and wipe them out in one swift go. That included the obvious candidates like Bruce Banner and the other Avengers, but in total, Jasper Sitwell had calculated that it would leave 20 million people dead. That's a lot of threats.
So why the urgency? Well, the knowledge of Thanos changed HYDRA's plans entirely: they had been happy to operate under the radar but they were forced to step “out of the shadows, and into the light" when the world they were seeking to conquer was under threat from an even bigger conqueror. So they looked to fortify their own position, hedging their bets on the Confederacy (wrongly), but also looking to get their house in order before Thanos arrived.
They were looking to wipe out the threat of anyone who would rise up against them in order that they could concentrate their resources on Thanos. They would achieve their aim to control the entire planet in a few devastating strikes, and their unified people could stand against Thanos as one. That wouldn't have done much good if he had the Infinity Stones, but you can see why they'd believe in the strength in unity idea. They're a Nazi splinter cell after all.
But what does that have to do with Strange? He wasn't a threat? Or WAS he...?