I believed it might because the misalignment shifts the chainline to the left by 1mm.

Yes, I tried loosening the cable and adjusting the limit screw. Still had the problem. As for the hanger, I thought it made sense to first check the rear triangle alignment before messing around with the hanger. From your reply it sounds like I should just ignore what seems to be a minor misalignment and tackle the hanger as the culprit.