In previous version of Godot I used post process shader as described in the tutorial but I was using Visual Editor so in vertex shader just plugged inverse projection matrix into model matrix output to make it always be in front of the camera. With the change of depth buffer now my quad is 1.0 away from the camera, which makes everything between camera and 1.0 to render without post processing.
Any ideas on how to fix that? (I made it work, but not sure if it is the right solution)