Tested on a desktop PC with NVidia card: rendering is corrupted with depth-peeling disabled (A), rendering is correct with depth-peeling enabled (B).

If texture interpolation is turned off, then display is correct.

for snName in ['Red Volume Slice', 'Green Volume Slice', 'Yellow Volume Slice']:
getNode(snName).GetDisplayNode().SetInterpolateTexture(0)

I took a look at scenario A. In the OpenGL2 backend the actors for the slices are not rendering into the depth buffer (i.e. glDepthMask(GL_FALSE)) because GetIsOpaque() returns false; see https://github.com/Kitware/VTK/blob/94dfcdac64c2e987155b216d39e6049fa1206e4b/Rendering/OpenGL2/vtkOpenGLActor.cxx#L59

In the OpenGL backend this code checked whether the actor's property's opacity == 1.0.

As a test, in the debugger, it looks like forcing those actors to be opaque (vtkActor::ForceOpaque) fixes the rendering.

Without verifying, the difference seen when disabling texture interpolation can probably be explained by the checks in https://github.com/Kitware/VTK/blob/94dfcdac64c2e987155b216d39e6049fa1206e4b/Rendering/Core/vtkTexture.cxx#L260

For reference, this was fixed in https://github.com/Slicer/Slicer/pull/586 / http://viewvc.slicer.org/viewvc.cgi/Slicer4?view=revision&revision=25394

I've tested this and it works well on NVidia and Intel GPUs, too. Thank you!