One other thing that Quirrell did was to portray the government of magical Britain as the opposition, since he and Harry agree that it's corrupt and incompetent. That made it easier for Harry to dismiss opposition to the plot as foolishness. It also bound Harry & Quirrell closer together in Harry's mind, and made their shared rationality salient.

But it could have driven Harry & Quirrell apart, since this is one area where Harry knows something about Quirrell's goals. They have talked about what kind of government would be best, and they disagree. They even had a kind of public debate about it. So why would Harry be so eager to join a secret organization to reform or overthrow the government of magical Britain, without at least worrying about what kind of government they're trying to bring about?

That's a worry that should carry over to Quirrell's actual plot. It's a very basic question: why is Quirrell doing this? What is he trying to accomplish? But one that Harry apparently never asks.