Answering to your and original question above: there are no poles (or axes of rotation) in the Universe. On large scales (think distances to include thousands and millions of galaxies each with billions of stars with even more planets) the Universe is uniform - isotropic and homogeneous [1]. It is expanding with acceleration in all direction in each and every point of its space, so there is no preferred direction thus in average we should have 50% of clockwise and 50% of counter-clockwise galaxies since orientation of those should also be absolutely random in average, unless something when the Universe was being created or evolving affected that balance.
Dumb question time continues: The majority of the solar planets rotate in the same way, and the majority of the large moons rotate in the same direction as their planets. I assume this is influenced by the rotation of the relevant accretion disks. And I assume this is common for stars within a galaxy?
I don't think the universe is considered to have any significant rotation, however. Is this due to scale for us to measure, and/or having nothing external to compare against?
That's exactly it. Solar systems and galaxies have net rotation, and maybe even galactic clusters.
But there is no reason to think that the universe has a net rotation. It could have one; you don't need a frame of reference to detect rotation. (The same way you feel centrifugal force.)
It would be huge if it were shown to have a net rotation. So huge that I take this claim with skepticism until heavily confirmed.
So it makes about as much sense to ask why 2/3rds of the galaxies are "upside-down" from our vantage point, because there's no clear reason it should be something other than 50% in a sample size this large?
1. https://en.wikipedia.org/wiki/Cosmological_principle