This results in the mule dragging the player around until they cancel docking. I assume the sudden acceleration of the player's automatic docking maneuver makes them think they need to match speed. There are two possible improvements here:
1) If a ship's order giver is trying to dock with it, it should stop rather than continue trying to follow.
2) Reduce the strictness of docking requirements to being within a small distance of a docking port and having relative velocity below a reasonable value. This would make it possible to dock with moving ships/wrecks, instead of being dragged until they stop.

relanat 5 May 2021:

I've seen this behavior in 1.9b3.
Moving towards a mule will make it shift and as you try to dock both playership and mule move away.
It isn't strictly linked to docking.
Sometimes just flying slowly over where the auton is resting will cause it to move slightly.