Per eye camera of OVR Camera Rig not working in HDRP or URP

Hello,

I am currently having an issue with using the per eye camera with the OVR Camera Rig concerning the culling mask. I am trying to have one item visible to the left eye anchor and not visible to the right eye, and a different item visible in the right eye anchor but not to the left eye. However, this does not seem to work in HDRP nor URP, and only in the standard 3D project, which seems to be due to the "use per eye cameras" setting not working properly the culling mask works for non-OVR cameras). Any insights on how this issue could be resolved?

This is using Unity 2021.1.3f1.