My understanding is that protein and DNA helices show the handedness that they do due largely to the intrinsic chirality of their components. Note that in natural biomolecules L-amino acids and D-nucleic acidssugars predominate. This apparently leads to a subsequent bias in their respective polymers.
I believe that it has been demonstrated that artificial alpha helices constructed of achiral amino acids demonstrate inversions between left and right handed forms- these then need to be stapled with extra molecular bridges to hold left or right handed orientation.
Thus, I don't think that there is a right-to-right or left-to-left association. In all cases, I think it's just that the biased handedness is baked into the structure of natural amino acids.