The IC argument is FAITH, not any particular incarnation of faith. For example, Obi-wan tells Luke he needs to trust the Force, when really all Luke needs to do is to TRUST SOMETHING... ANYTHING -- himself, the Force, R2D2...it doesn't matter. So your MC has to have faith in something even if the IC is saying have faith in something else. The point is that the conversation is no longer about Disbelief, which was the source of his personal conflict. The 'conversation' has moved on and the MC Problem becomes a moot point -- it is of no consequence any longer because that story (argument) is over. THAT IS THE MOST SIGNIFICANT PART OF THE CHANGE. It may turn out that Faith isn't the answer either, but the fact that the MC has released himself from the black hole created by the blind spot associated with the MC Problem is what allows the MC to move on with his life.
Blue pill vs. Red pill isn't the right kind of comparison. The real issue is perceived world versus reality (perception v. actuality), but the pill representation is only meaningful to the MC (Neo) if he can conceive of the difference between the two, which he can't because he's not ready. What the pills represent at that point in the story is the first step TOWARD being able to know the difference between the two. Just like your character, Neo has to get past the distractions of the pills so that he can let go of his disbelief and have faith that he could be the ONE. It just so happens that he is so we have a happy ending, but you could have had an ambiguous ending like that of Inception where the MC has changed but the audience doesn't know if he ended up in reality or perception land. For the MC it doesn't matter because that was not his personal problem.