The zodiac is already out of synch.

In 125 million years, chances are that we would be greatly out of synch with the stars we consider our neighbors today. But what the night sky would look like is not easy to predict, because we’d be in a new neighborhood, some of which would be familiar, much of which would be strange and not known at this time.

The view of the night sky would be considerably clearer given the likely absence of anthropogenic light.

I did a Web search and came across this article talking about how the sky will look in 5 million years. If all the stars rotated at the same rate around the center of the galaxy then everything would look the same, but the article says that some stars move in other ways. Also some stars disappear, as will happen to one of the stars in Orion, which is expected to go super-nova. Closer stars will have appeared to have moved further.

The article says that the current constellations will no longer be recognizable in 100,000 years, so it will be necessary to keep updating the zodiac.