The Fiddler Classic has a Composer option called "Automatically Authenticate" (which auto-converts your user@pass to auth headers), but this option is not yet available in Fiddler Everywhere. The team is currently researching and planning to provide more built-in authentication support options (including upstream proxies with authentication and other auth options like the one mentioned here).
Converting this thread to a feature request, more users can upvote it.
I receive the a 401 unthorized when replaying a request or using Execute in Composer when the site I’m hitting uses Windows Authetication (NTLM). In How do I configure Fiddler Everywhere to login using NTLM with it receives a 401?
I don't have this problem in Fiddler Classic.