There's a Perfectly Good Reason for Doctor Strange to Hate MCU Iron Man
From the moment MCU dived into crossing over its various superheroes in the first Avengers, it thrived on creating conflicts between said superheroes.
Sometimes said conflicts were caused by villainous manipulations, sometimes by naturally clashing character traits. Sometimes they were resolved in the same movie where they were introduced, sometimes they lingered.
The latter was true in both cases for the conflict between Doctor Strange and Iron Man. Or, to be more specific, for Stephen Strange hating Tony Stark. This enduring negative feeling might feel bizarre and introduced just for the sake of having a conflict, on the first glance. There was no rational reason for Strange to have a beef with Stark.
But that does not mean he did not have a perfectly explainable reason – just not a rational one, but whose emotions are fully rational at all times? You see, Tony Stark had plenty of character development that allowed us to see him in his more vulnerable and self-reflective moments…
...mostly in his own movies, when none of his Avenger teammates were present, and sometimes when he was isolated from nearly everyone, as in the beginning of Avengers: Endgame.
When in public, he still wore his old persona of a self-confident, sometimes to the point of arrogance, cocky, abrasive, big-ego smartass, as if it was his second layer of armor under the Iron Man suit, all the way to his very last words.
And that was almost exactly Stephen Strange acted before his magician days, when he was a world-class surgeon. Sure, elements of that demeanor never completely left him, but he had changed much more than Tony in the process of becoming a superhero. Stark was a walking, talking unpleasant reminder of how Strange himself was before getting a taste of humble pie, so it is no surprise that his existence rubbed Strange the wrong way.
Well, of course it is also possible that Stephen simply found himself deeply irritated by the man with facial hair groomed in a way obviously very similar to his own, but not quite as neatly, and took Tony's mere presence as a challenge to himself and his impeccable style. Hey, again, emotions are not always rational.
One wonders what Doctor Strange might be thinking of Iron Man now, upon being forced to fill practically the same shoes on the Avengers team, and if he's going to voice those thoughts in any of the following movies.