OnMouseDown does not work on a monitor while having a VR (XR) setup

I 've set up a project with an XR Rig using new XR Management.
The second screen (PC monitor) renders a camera with a Culling Mask placed on the scene, so a person can spectate from some othe point than POV.
I want the spectator to be able to click on the Game Objects. I use abasic script on these objects with colliders, that goes like this:

Code (CSharp):

1. public class ClickableObject: MonoBehaviour
2.     {
3.  
4.         public void OnMouseDown()
5.         {
6.             Debug.Log("Pressed object", gameObject);
7.         }
8.     }

When I run the project and click on the GameObject nothing happens.

However, if I select the camera while the project is running and change occlusionCulling parameter (does not mater off or on) - objects start reacting to clicks. This trick helps ONLY if I manually change this parameter in play mode. If I set it beforehand it won't make any difference.

I even tried to add a script that automatically ticks occlusion culling on and then off after a second after launching the play mode, but that does not help - only clicking in the inspector helps.

Please advise.

 

Changing priority of the camera from 0 to one somhow solved the issue. Could someone please explain me why did it work?