Ok. I think I figured this out. Thor and Iron Man both gain quite a bit of respect for Cap when Thor tries to hammer him into the ground.
He stands up to a demigod and throws a chunk of metal at his face. And most definitely commands
their obedience. The reason Stark has a change of heart midway through the movie is the same reason Cap calls Tony out about not being a hero. They are under Loki's influence for roughly the next 40 minutes. Then, once Stark is back of sound mind, he assures Loki that Cap lives up to the legend.