Shimmer due to motion aliasing of sharp edges is a problem on all digital displays. It is especially bad on low resolution screens like those found in VR HMDs, and reaches almost epic badness on Gear VR and Go with the new Oculus apps that use foveated rendering. There are ways to mitigate it, and Oculus should try hard to find one that works on those platforms.
CORRECTION The problem is only in the VR mode of Oculus Browser. 360 Photos, Gallery, and Gala360 show no trace of shimmer, on the same images. So foveated rendering is not to blame. But Browser definitely has an aliasing problem that needs to be fixed.
I have only GearVR and Go headsets. Every 360 photo I view on Oculus Broswer shows severe motion aliasing. Example: https://vizor.io/tksharpless/js-cornfield-test/ (stereo 3D) There is no shimmer on the grass when I view this same pano in Oculus 360 Photos, which doesn't use webGL. I would be interested to know whether this problem affects the desktop version of Oculus Browser.