supernatural or mysterious?

If experience determines one's reason to follow or form a religious or spiritual (I am not partial to the word supernatural) view of reality (or even a naturalist view), this experience can be the evidence needed to subscribe to a certain view, but the experience, especially in the instance of spiritual views, is either purely subjective or such that only a select few can relate to; and therefore, what place do spiritual views have in the public domain of policy making or institutional curriculums? Likely none. To put this another way, there is 'natural' experience and 'supernatural' experience; everyone experiences what is called 'natural' (experience that is objective, and has science/sensory based evidence), and therefore 'supernatural' discussion should likely be left out of the 'public space'. The idea of the 'supernatural', however, is an idea of the naturalists, as those that the naturalists refer to as supernaturalists consider their so-called supernatural beliefs to be natural.

Nature is mysterious, as the professor assured. What we experience cannot always be explained or understood clearly or entirely, but does that make these experiences 'supernatural'? What is the difference between mysterious and supernatural? Or the difference between an event that is mysterious and an event that can only be taken on faith? Should the mysteriousness of nature or the acknowledgement that we are prone to having experiences that science cannot entirely explain (even if the potential to eventually understand is there) be left out of the 'public space', if these events are very much apart of nature as we currently experience and attempt to understand it?