Apparently this is currently a ‘known’ issue (reported here previously) that Sonos/Apple are already investigating - the workaround suggested is to try to use an iOS device for the Apple Music Service setup until a fix is released.

See this thread too: 

https://en.community.sonos.com/music-services-and-sources-228994/can-t-add-apple-music-on-android-sonos-app-6861876

I’m also having this issue. I don’t have an iOS device so really need this fixed.

Please read the thread linked in the post immediately before yours. 

Experiencing same issue. Screen blanks whether I select 'existing account" or "create new account".

Tried resetting, getting newest updates, other devices, etc. I do not have an apple device.

Maybe see this LINK which perhaps might go someway to solving your issue until a fix is in place.

I am a former spotify customer. There were two reasons I switched. 1) Sound quality of Apple is superior. 2) Apple’s library had a greater selection of 20/21st century contemporary classical and avant garde composers I follow.

Sonos is taking there sweet time fixing this problem in their android. It just keeps me from purchasing any more sonos products until the issue is resolved. 

Unless it’s not an issue on Sonos’ side of things, but instead an issue with Apple’s response not conforming to requirements. We just don’t know, since Sonos would be unwilling to throw Apple under the bus….but Sonos does normally fix bugs like this in their own software much more quickly. 

I’m worried right now that there’s nothing Sonos can do about it, and it’s entirely on Apple’s side of things. 

seems like they finally fixed it. I just tried logging into Apple Music on my Android and it straight away worked for me. Awesome