Has celestial navigation been materially impacted by the imperfect nature of celestial reference frames over time?
The best inertial frame is that which is comoving with the cosmic microwave background. There is a notable dipole in the microwave background, the result of the Solar system's motion relative to it. The invariance of this dipole provides evidence that the frame of the barycentre of the solar system is also a very good inertial frame. 

This is of no significance to navigation, either by the stars, or among the planets. 

Within the solar system, the sun's gravitation influence is dominant. While the sun is orbiting with the galaxy, a space probe is also orbiting the galaxy, and the variation in gravitation due to the galaxy is extremely small. Galactic tides are several orders less significant than photon pressure, various quadrupole effects or the influence of other bodies.