Win10, Nvidia 1070
Tested in Blender 2.80, 2.79b, true in both.
Relatively minor bug.
The camera can acquire skew from parenting relationships that lead to it inheriting scale that lies outside of its basis vectors. This skew affects renders. This is inconsistent with how the camera handles basis vector scaling, which it removes for render. That inconsistent behavior is why I consider this a bug.
To reproduce, create a camera, parent it to something, scale the camera's parent non-uniformly (different amounts in different axes), make sure that the camera has local rotation, but not local rotation at exactly 90 degree intervals, render.
Suggested fix: either cancel out skew by recreating camera basis vectors on the basis of Z, average X+Y vectors, or allow even uniform scale to affect the render. I would prefer the latter personally, as it would allow greater artistic freedom.
Workaround: give the camera a limit rotation constraint (no axes have to be enabled, and limits of -180,180 are fine.) Which could be it's own bug report, but even more minor-- copy/limit rotation/scale constraints don't seem designed around the possibility for skew, and seem to instead just rewrite the matrix components they assume rotation and scale to have affected without recognizing that inherited non-uniform scale can affect other components of the matrix.