Kerbal Space Program

This effect appears to be conditional on whether you're orbiting at less than 750m/s.

General consensus is that this is related to the Krakensbane threshold. See page 3 in the linked thread.

Requesting that this bug be moved to a higher priority.

I, as an independant observer (not having the patience to test the bug right now, maybe tomorrow), would believe that this is at most due to floating point errors. However, from a realistic point of view, Kerbals being happy/scared/generally moving around would destabalize the ship.

I would mark this as not a bug, because it could potentially be intended behaviour, but I'll let someone else make that call.

However, I personally would either keep the current priority or downgrade it, since it doesn't affect the game a whole lot.

This most definitely is a bug. I can confirm it in a modded save (where the mods I have installed would not affect this side of the game), and others in the linked forum thread have reported the same stock behavior. This bug affects manned and unmanned spacecraft, and primarily affect low gravitational parameter bodies such as the Mun. In fact, this bug makes docking around the Mun nigh impossible, as not only does this bug create phantom torques, but on more massive vessels actually can be seen applying phantom translational forces as well. Sometimes the forces applied overcome any RCS forces being used to try to cancel them out, resulting in the wanton waste of RCS fuel. You can see the translational behavior best by zeroing out the relative velocity between two spacecraft and then tapping on and off time acceleration to zero out any rotation. The kraken likes to pick a direction and stick with it, for the most part. I would recommend giving this bug medium priority, because at this stage in the game something as basic as orbit around the Mun should not be this frustrating!

I can state that I don't have trouble docking near Mun in an unmodded install. Additionally, the use of SAS would cancel out the effects of the bug as you report it (know that you don't need to use RCS for this, I tend to prefer using reaction wheels for direction).
As I see it, the bug is very easily worked around, given that I haven't encountered it in the situation you describe.

Right now, I'm starting to think it might be related to how far you are from the center of the body (radius + altitude). Lesser distance == greater effect. This would be because of how the navball reorients itself to the body, and if you are travelling, you are indeed getting a differing angle.

I'll check what MechJeb says about my angles later in a geostationary orbit.