I think this may be a subtle reference to what is usually called "relativistic beaming" or "Doppler beaming" [0], though I normally associate this effect with matter that is moving quite close to the speed of light.
perihelions [1] phrased it best - a galaxy spinning clockwise is just the mirror image of one spinning counter-clockwise. So why should mirroring change brightness? I don't really understand why Doppler beaming would cause this (though one of the papers did also mention it).
The other question is - what does the rotation of our own galaxy have to do with it? Let's keep the Solar system as is, and mirror the rest of the Milky Way around it, so that it is now spinning the opposite direction. Why should this affect the apparent brightness of other galaxies? Especially since the Solar system is effectively moving in a straight line, on the scale of a human lifetime.
This is only obvious when you yourself are not moving on a curved trajectory.
In GR curved trajectories lead to "weird" observations. For instance, I'd expect the side of the remote galaxy that is closer (visually, for you as an observer) to the center of your galaxy to be gravilensed slightly more than the other side. Because the effect is non-linear, it does not just compensate when sides are reversed.
P.S. Not claiming this has any significant effect on the described phenomenon, just that mirror symmetry does not apply.
[0]: https://en.wikipedia.org/wiki/Relativistic_beaming