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.

relanat 3 Dec 2022:

I have noticed that this happens a lot more with the standard game 330M mule than larger mod autons (1.9.2).
The Big Mules mod has 550M and 770M Mules. The 'dragging' doesn't happen with the 770M IIRC and rarely happens with the 550M. It is very common with the 330M.
Possibly higher mass or size XML values reduce this behavior. The 330M ShipClass has mass=2 and size=16. The 550M and 770M have 3 and 18 and 4 and 20 respectively. Time permitting I will give a very light auton a trial and see what happens.