I have a staging server that uses basic HTTP authentication to restrict access. After a user gives their credentials, they are able to access the site just fine with the exception of the site's manifest.json - it appears that Chrome is not passing the credentials for the domain along with the referrer request for the manifest, which then causes a 401. You can, however, hit the file directly just fine.
I haven't been able to find much information on the subject, though I'm curious if this behavior is intentional.
To replicate, set up a server with basic HTTP auth. Create a manifest.json as well as a basic html file that links to said manifest. Try to hit the page, get the login prompt, and fill in your credentials. When you successfully load the page, check your console and notice that you get a 401 for the manifest. Then try to hit the file directly and notice that it loads.
I've validated this with both Windows 10 and Linux (not sure the specific version at play - simply had a coworker test for me).