SRP Repo: Issue 1604

What happened?
In my project I have three cameras:

Skybox Camera (Clear Flags = Skybox, Depth = 0, Culling = Nothing)
World Camera (Clear Flags = Depth Only, Depth = 1, Culling = Everything But Player)
Player Camera (Clear Flags = Don't Clear, Depth = 2, Culling = Player)
The skybox camera is there because rendering the skybox at the FOV specified in the world camera looks terrible. The player camera has nothing to do with this issue - disabling it still causes the problem to happen.

This setup works fine with just the lightweight render pipeline, but adding a post-processing layer (even without any volumes or overrides specified) causes the skybox to stop rendering. Here's what it looks like without a post-processing layer:
https://i.imgur.com/rOKNW6P.png

And here's what it looks like with one:
https://i.imgur.com/0tqH20F.png

Poking through the frame debugger it looks like the skybox does end up drawing:
https://i.imgur.com/idmASYH.png

But is immediately tossed out when the world camera begins drawing:
https://i.imgur.com/XLTAAwd.png

Which package (Shader graph, LW, HDRP, Core...)?
Lightweight Render Pipeline

Unity template or github source code?
Unity template.

Which package version or branch (1.1.8-preview, 2.0.0-preview, 2018.1, 2018.1-experiment, 2108.2...)?
1.1.11-preview

Unity version, operating system, target platform (standalone windows, mac, iOS, PS4...)?
Unity 2018.1.1f1 in the editor on Windows.