Sad but true. I'm quite excited to learn that when you put in a date and time in Stellarium that goes back to the time of Ptolemy's Almagest, it actually adjusts for the precession of the equinoxes.
As the two screen grabs below show, Polaris is way off the celestial north pole back in the year 138AD.
Stellarium screengrab - 2017AD
Stellarium screengrab - 138AD