Minecraft Version

1.16.x

Version

1.98.2

Details

So, to understand this bug, you first need to know that in vanilla MC, an armor stand can be tagged "marker", which is supposed to prevent any and all physics interactions with it (water, pistons, etc).
By chance, I came across the fact that turtles were sometimes pushing around my marker armor stands, which is not supposed to happen.
While it seemed inconsistent, I eventually figured out that it happens when the turtle is trying to push marker stands that are floating, and only while travelling to the North or West directions (as defined by f3).
They also can sometimes be pushed exactly once by .5 blocks in the East and/or South directions. Whether or not this happens, further attempts to push it in these directions by the same turtle or different turtles result in it phasing through like expected, while they can still be pushed North or West a seemingly unlimited number of times.

To reproduce:
Summon an armor stand with the tag Marker:true somewhere just above the ground. The x and z coordinates can be integers or floats, but the y coord MUST have a value after the decimal point. (note, 4.0 does not work, but 4.001 does.)
Place a turtle on the ground just in front of the armor stand. Tell it to go forward 4 blocks.
Re-summon the armor stand, exactly as you did before, and place another turtle facing the armor stand in a different direction.
Repeat for the other two directions.
In theory, you should get this:

(taken while facing north)

Note that the armor stand's position can be difficult to determine visually. To make sure the turtle is/should be lined up with the stand, I would either use the Pos tag to check or kill the nearest armor stand to me (e[sort=nearest,limit=1]) and then respawn it with command history. Also, remember that an integer on the x and z coordinate is read as that coordinate + 0.5, to center it properly. Doing, say, -237 vs -237.0 changes where it is.

No logs because "entity was moved" is not a logged event.
This was done in an install with just forge and the latest release of CC btw.