I am trying to reconcile two facts:
That galaxies' comoving velocities are generally close to zero, and
That the universe has no preferred reference frame.
Galaxies seem to move very little relative to each other, aside from motion due to the expanding universe. This is why astronomers can use redshift as a measure of distance. However, this suggests that there's a preferred reference frame -- the one we're in! In every other reference frame, galaxies must have a non-zero comoving velocity on average.
It seems like there are a few possible resolutions to this:
The universe DOES have a preferred reference frame, and we currently occupy it. In any other reference frame, galaxies would all have a significant peculiar velocity in the same direction. For example, if we launched a ship at 0.5c right now, observers on the ship would see a blueshifted universe in front of them and a redshifted one behind them, and could conclude that they were in a moving reference frame.
To an observer traveling near c relative to us, the universe looks exactly the same: The galaxies they see ALSO have very little comoving velocity. In this case, the relativistic observer sees the same thing we see and there is no preferred reference frame
There is a preferred reference frame, but only locally -- where "locally" means in the observable universe only. Over the entire universe, galaxies have a wide distribution of peculiar velocities. However, before inflation occurred, small regions of matter already "agreed" on a shared reference frame. Then, after inflation, the entire local universe became one of those regions with a preferred reference frame.
I feel like the third explanation is the most likely. Is this the right conclusion?
(Context: I'm currently taking my first grad-level cosmology course, and this question has been itching at the back of my mind for a few weeks.)