Doesn't the distance of stars disprove the young earth theory?

Welcome PEIN.Hope you enjoy this site and will contribute, teach and learn with the rest of us. And this well known fact, along with its well known mis-interpretations, answers the OP (opening post) in what way?Are you thinking that the light we see from galaxies billions of light-years away has been somehow time-shifted to show great transit age but in reality is but a few thousand years in transit?This is the "Science" side of this forum so please be specific with attributed evidence.

On a practical level you are correct.But, to be nit picky, if you and PEIN are ever in relative motion to the other at any time then, yes, time passes differently between you. The dilation is so minuscule, however (on the order of a few millionths of a second), as to have no practical effect.