Is it possible to hide extension resources in the Chrome web inspector network tab?
Not quite the solution I was after (I'd have preferred a global setting), but there is now a way to filter out requests from extensions, as mentioned by a commenter on the issue I originally opened.
In the network tab filter box, enter the string -scheme:chrome-extension (as shown below):
This is case-sensitive, so make sure it's lowercase. Doing this will hide all resources which were requested by extensions.
An Incognito Window, can be configured to include or exclude extensions from the extensions page of Chrome settings.