We use Right Hand Rule in calculating Torque not because that's the direction torque is pointing in the real, physical world, but because it's a convenient way to indicate the "sign" of the rotation and its axis, and as long as we pick one coordinate system and stick to it, everything works out.
I think (I might be incorrect) we use the Right Hand Rule in Electromagnetism arbitrarily, but it happens to be very convenient only because of the right combination of Benjamin Franklin's arbitrary choice for designating current flow and the way our magnetic field was aligned at the time of the convention choice for North. But essentially, it is arbitrary -- if Benjamin Franklin had chosen current flow to match the flow of electrons, we'd either use another choice of axes or say that the magnetic field is negative.
What I'm saying is that I don't think that nature itself is inherently "right handed" in this situation.
Is there any case/situation in physics where the Right Hand Rule and choice of coordinate axes is not arbitrary, but rather inherent in nature itself? How so?