With regard to neutrinos, what if they are mostly not supposed to interact and we should be barely aware of their presence due to 'other causes'.

Strange idea but here goes. In 1999 the superluminal appearance of a jet emanating from M87 in the Virgo super cluster gave the optical illusion of light travelling at four times the speed of light.

Well that can't be right as it would be in disagreement with special relativity. So what exactly would an energy particle travelling outside our frame reference with respect to the speed of light look like. Well probably a highly energetic lump of some sort perhaps and probably a very difficult particle to give attributes of mass. It would be one that mostly doesn't interact and when just barely interacting with another particles causes an interesting cascade of assorted energies.

Because it is outside this reference frame with respect to special relativity then we are not within its frame either and are unable to interact mostly. The energy equivalent for a neutrino would exceed the most energetic of known particles and may just pass because of an inability to catch it.

Just a passing thought.

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"Nature is obliged to let reality determine its laws, whereas mathematics is under no such constraint."