Outlook 2010 prompting for credentials when connecting to Exchange 2016..
After a load of testing and MS involvement
We have been operating on the expectation that the December cumulative update of Windows 10 https://support.microsoft.com/en-in/help/4053578/windows-10-update-kb4053578 has an issue introduced to create an auth prompt in the OAB download in Outlook as it uses the Background Intelligent Transfer Service (BITS)
Testing showed on several computers that the installation of December or the January update https://support.microsoft.com/en-in/help/4056888/windows-10-update-kb4056888 triggers the prompt
So these hotfixes appear to be causing the issue.
Before you spend hours troubleshooting Exchange like we did, check those hotfixes.
For the moment I think we're going to disable the BITS service.