Hello Loyd
no, it is certainly not due to a loose spindle.
One of the very basic principles of face milling is that the cutting forces are always uniform during face milling. When the milling direction changes, as shown in Eddy's example, the cutter stops. Both the stop on the material surface, nor the move out of the material and back in, to have the stop outside the material, is according to the textbook of face milling.
If I stop on the material, the milling is minimally deeper at this point, if I move over the edge of the plate to set the stop outside the material, the cutting forces change when moving out, and when moving in, the increasing cutting forces can cause vibrations.
The cutter must always be constantly engaged.

Another thing that speaks against the changing tool paths is my base plate made of PMMA because I mostly cut PMMA . In principle, face milling should always be performed in constant force. In the area of an overlap, there is different heat in the pmma where the cut is made than in the overlapping area. As a result, a touch more is always cut away. With alternating tool paths, this area is in the middle of two tool paths. This must not be the case either.
I know it depends on the mill or the material. A wobbly router may have problems with the spindle wobbling. But then the mill also does not manage to stop the cutter. If I'm milling an MDF or wood, none of that matters. But if I'm milling aluminum or PMMA and want to achieve a really smooth surface, you shouldn't alternate toolpaths.
When I mill cast PMMA blocks, I see the difference in how much I have to grind before polishing.
ralf