The major plot wasn't HYDRA doing evil things because they're HYDRA. It was that HYDRA had infiltrated SHIELD to such a high level (to the point that they were in charge of SHIELD) and nobody noticed, because HYDRA and SHIELD agreed on a fundamental level. Insight seems like such a great idea to prevent suffering and misery that nobody asks questions, and nobody knows what names are going to be on kill lists or for what reasons. The higher ups know better regarding how to identify the bad guys. Even when Cap is accused of treason and labeled a threat, nobody asks questions. They're afraid to rock the boat.
This movie focuses on the one aspect that was glossed over the first Captain America movie, which is the reason why Steve Rogers was chosen for the super soldier serum in the first place. He didn't need to be strong, fast, have good eyesight, or be in good health. The serum would take care of that. What the serum couldn't give was courage and a moral compass.
Everyone in the movie is ruled by fear: fear of the "bad guys," fear of being reprimanded by the boss, fear of losing their reputation, fear of their secrets being discovered, and so forth. All that is required for evil to win is for good men to do nothing, and everyone is paralyzed with fear. Everyone except Steve Rogers, because Steve Rogers can not be cowed or intimidated. Steve Rogers has been standing up to bullies since he was a 90lb weakling. He does not fear pain, hardship, or damage to his reputation.
It is up to Cap to ask the difficult questions, and to draw the line in the sand. The struggle in the movie is getting Steve Rogers to realize that. In a world where so much has changed, all of which he missed, he wants to lead to a simple life of a soldier who follows orders. When his organization turns on him, labeling him a traitor and making him a fugitive, he doesn't know who to trust or even where to start. The real conflict is Steve Rogers accepting that he's Captain America and not Private America. It's not about who he's able to trust, but who he can get to trust him.