In one of the messiest foul-ups in Marvel movie history, Doctor Strange's arrival in the MCU opened a fairly big plothole thanks to some foreshadowing specifically designed to foreshadow it.
Along with the Sorceror Supreme being hinted at thanks to the appearance of magical relics and mystical dimensions and forces elsewhere in the MCU, the first explicit mention of his existence came in Captain America: The Winter Soldier. In that film, we saw the treacherous Agent Sitwell reveal that HYDRA's infiltration of SHIELD had culminated in the development of Project Insight.
HYDRA designed that programme to monitor targets and potential threats to their planned global dominance. Both Bruce Banner and Stephen Strange were name-checked along with Tony Stark and a hint at Moonknight. Their technology was developed based on tracking behaviour and online activity (basically, they made Facebook and weaponised it, just like Mark Zuckerberg definitely isn't) to identify anyone - super-powered or otherwise - who could stand in their way.
Stark and Banner make a lot of sense as targets, since one is Iron Man and the other is the Hulk. Even the Moonknight hint could make sense, since he could be operating in Egypt. What makes no sense is why HYDRA would be interested in a conceited, arrogant surgeon who doesn't have a selfless bone in his body and is obsessed solely with his own reputation and professional record.
At the time of HYDRA tracking Strange, he's as far away from being a superhero who could stop them taking over the world as possible. In actual fact, he's probably the kind of person who would work for them if they could guarantee fame and glory. That's how much of a dick the script makes him. His bank details and online history (and anything else the Insight algorithm tracks) wouldn't indicate anything other than a self-interested playboy with a penchant for sports cars.
There is also no way HYDRA's algorithm could plot that Strange's arc would change him so fundamentally (which is the ENTIRE POINT of the Doctor Strange movie plot). The only reason The Ancient One thinks he has good in him is because she's seen the actual future and sees him heading on the right path up to her death. The idea that anyone could look at Strange as he was and predict that he'd have a car crash, ruin his career, waste his wealth and end up being a Sorceror (when the Sorcerors exist in SECRET) is just ludicrous.
And of course, you'd think that HYDRA would have identified more sorcerors than just Strange if they were aware of them existing... So, there's definitely a problem there.
But, what if they weren't tracking Doctor Strange based on his status at the time of Project Insight? What if they'd tracked a future version of Strange who had reappeared elsewhere on the timeline using the Time Stone and been picked up by Project Insight. Given their access to facial recognition and the other technology, the sudden appearance like that of an individual with the potential to disrupt reality so much would almost certainly flag up their systems.
Remember, Insight was built partly out of the agenda to track threats that could appear in the same way Thor did - it would be built on SHIELD technology that was developed precisely for that purpose. Given that Strange could theoretically travel anywhere on the timeline with the Stone as long as he had it, he could have jumped back in time to the period HYDRA were monitoring.
And that could actually fit in with another existing theory. Previously, we've discussed how Agents Of SHIELD established an explanation of how HYDRA knew about the coming threat of Thanos in season 5's "The One Who Will Save Us All." That theory suggested that HYDRA were looking to take out threats before Thanos came, in order to concentrate their focus on defeating him and not those who would rise up against them. All for the Greater Good, of course.
But what if HYDRA had identified Strange as a target because of his use of the Time Stone, which would have been flagged specifically because of their knowledge of the impending arrival of Thanos after their tip off?
It could well be that HYDRA's algorithm saw this future version of Strange appearing as enough evidence to assume that Strange in the present was a threat who needed to be eradicated altogether. Which is the only way anything about him being identified by Project Insight makes any sense at all.