Since upgrading to 10.14.3 (Beta 18D21c) on my Mac Pro (Late 2013), iTunes (12.9.2.5) asks me for the password to my account in iTunes.
A bunch of IOS devices are connecting to iTunes via WiFi, and I have a large iCloud Music Library, but even if I simply cancel the password request, everything works fine. I can play and add Apple Music to my library, and this is without typing in the password when requested.
If I type in the password, and then shut down iTunes again, I am not requested the password if I login to iTunes again immiediately following.
To troubleshoot, I logged the iTunes account out entirely, and then back in again, and still I am asked for the password, if I shut down iTunes and wait say 15 minutes to open up iTunes again...