When you are working with a very finite amount of information it isn't hard to think alike Wait (and hope) for when Strange gets to do more than just be in the background firing a bolt at something and then we might diverge.
I have a dreamed of scene in the MCU when Iron Man meets Strange, and comments on him copying his look, and Stephen answering something like "I've had this beard longer than you've been shaving." I admittedly didn't read Iron Man before the MCU, so I can't verify this, but it seems Tony Stark only got the goatee after RDJ looked so good in it. So they really ripped off Strange's look, IMHO.