The burden of proof is on those who claim there is a factual basis for 'supernatural' events.
Attempts to uncover objective evidence has so far failed 100% of the time. It is not open-minded to reserve judgement on the supernatural. It is obtuse not to be deeply skeptical.
There are tons of things that fall into the category of supernatural and all should not be treated equal. That is also because once something 'supernatural' is understood, then it's no longer super natural. If mild form of telepathy is one day proven to be scientifically based and rational explanation, it will no longer be 'supernatural'. If telepathy or a form of it is real, if it was based on brain waves and perhaps operating similar to a radio signal, or something that has a scientific base that is much more different than saying spells and having no scientific explanation. It is not obtuse to be deeply skeptical, but it IS obtuse to be so skeptical as to write it off and never explore scientific methods of research into it again. (especially if can think of possibilities of rational explanations, such as telepathy example).
Time is another thing, time is not linear. Gravity, black holes, speed of light, we KNOW it can be manipulated. Maybe things such as premonitions are the mind interacting with time beyond ways we can understand at present (IF any of them are real vs coincidence or illusion).
I think it is good to be very skeptical, but not so extreme that future research will never happen when some things can have a true basis but we lacked the technology presently to detect or properly research.