I tried signing out but nothing ever happens. I see a little gray flash of color indicating the button/link was pressed but that's it.
Several force closing of the app as well as several full phone reboots did nothing except allowed me to stream one song then nothing else. Also, pressing the "Radio" button at the bottom did nothing. Just got the loading screen.
However, once I got to my office and connected to our (relatively slow) WIFI network everything worked great (albeit after another reboot). Beats 1 loaded almost instantly, I streamed random albums and playlists. Life is good!
Then I decided to test the cell connection again. I forced closed all the apps, disabled WIFI and performed another full reboot. But I didn't launch Apple Music right away, I unlocked the phone then let it sit for about a minute or so just so I didn't immediately weigh the phone down with an immediate request. To my surprise and my satisfaction everything worked!! Wish I could explain what happened. For all I know Apple fixed the situation so all my reboots and such didn't really do anything. Like adjusting the radio in the car hoping for a better signal. You think you fixed it when you just drove outside of the dead zone you were in a few miles back.
Hopefully everyone else is okay. I can only pray this doesn't happen again. It was really, REALLY frustrating. I wanna love Apple Music and I know it has some UI/UX flaws but if I can't stream music when I tap on it that's a major problem. If Apple Music wants displace Spotify at the very least the service needs to be reliable.