The plastic agitator doesn’t move but the shaft does. I figured the plastic splines in agitator were stripped. I can’t for the life of me get the stud/agitator shaft unscrewed. I actually cut off most of the plastic agitator bell to get to shaft with a pliers but that bolt will not come loose! Also, the agitation (shaft) is weak so Im assuming Im dealing with more than just a stripped agitator. I already have the replacement plastic agitator assembly with the stud but I can’t get the old one out… Should I try a vise grips and anti-seize on the stud to get it loose? Or am I going to have to dig deeper and start taking the mechanical stuff apart?
I know its old, but it was free! 
everything else works, I just thought Id try my hand at fixing something - I like to solve problems and I since it was free I figure "why not".
use washer to loosen bolt start cycle and keep socket wrench on bolt to loosen. I have the same problem you describe I want to know if new agitator solves problem