Great post Walker, please forgive the brevity of the response, as I’m on a phone. My only criticism here would be with your word information. I think you are looking for the word evidence (or reason). To which, the point of statistics is to provide a way for us to reason about information.
Whether using Bayesian or Frequentist modes, we are trying to evaluate how much evidence the given information (data points) provides. Understood as such, faith and reason are in conflict by definition, since faith is believing in a proposition without evidence.