It seems like Windows 10 firewall is hard-coded to block access from managed apps to the localhost.
No matter what firewall exception I add, as soon as I enable the proxy to any localhost port (Fiddler or any other app running locally), none of Windows managed apps can access the Internet. Store, Maps, Mail, Edge, etc. - all get a "connection timeout" error.
The ONLY solution is to (1) turn off the Windows Firewall and (2) then stop the MpsSvc service.
WTF Microsoft!