The Full screen shader graph target that is designed to be used with the full screen renderer feature has properties for setting stencil behaviour. These settings do not seem to have an influence when the shader is drawn using the Full screen renderer feature. 

Steps to repro:
# open attached project
# Observe that the renderer is set up to draw the red sphere with stencil value 1 with render objects
# Observe that the "StencilPost" shader graph is set up with "Equal 1" 
# Observe that the full screen renderer feature (added to the renderer) renders with the stencil post shader.
# Observe which part of the screen is getting the pattern

Expected: Only the red sphere gets the pattern

Actual: The entire screen is covered

As a sanity check I added a quad in front of the camera with the same material as the full screen renderer feature. This quad will render if "Quad Post" is enabled. The quad behaves as expected (remember to turn off the Draw Stencil Post).