Has celestial navigation been materially impacted by the imperfect nature of celestial reference frames over time?

In this video on inertial reference frames, it is mentioned that the stars are humanity's best inertial reference frame: the earth experiences a subtle acceleration relative to the sun due to the earth's own orbit and rotation; therefore the earth is only roughly an inertial frame. But, the stars are relatively fixed, they say.

However, the stars in galaxies move relative to each other--I assume many with some sort of rotational velocity and therefore acceleration--and galaxies themselves are all slowly moving away from one another, perhaps even with centrifugal acceleration of their own.

Has this acceleration been great enough that humanity has needed to update navigational tools that rely on the assumption that stars are an inertial reference frame?

Is it possible that every observable object in the universe is in fact accelerating relative to an unobservable reference frame?