I was able to fix this issue and wanted to share how I did it just in case it could help someone else. 

I too experienced the dreaded Can't Sign in due to "Network Problem Detected".  I spoke with Sonos Support for 2 hours and they could not fix my issue. 

Here were the symptoms - When I try to sign into Sonos, I am presented with the spinning wheel with the error listed above.  I am able to play music from my connected services (Amazon Music, Pandora, etc.) BUT only from my favorites, not by selecting the streaming services in the Musical Note tab in the sonos app.  Additionally, my alexa enabled sonos speakers will confirm my verbal music request with a response of the music it will play, but no music plays. 

This is true across ALL 5 of my iOS devices.  However, when I downloaded the Sonos Windows app, everything was there and working perfectly (except for the Alexa capability).  That is when the Sonos Support rep said it is an iOS issue and contact Apple. 

The fact that I can see the speakers and play music to the speakers made me question that it is an iOS issue.  It really sounded like a network issue that is preventing Sonos from reaching outside of my network, even though we tried everything imaginable to fix it. 

My infrastructure is a mesh network, (Arris Surfboard W30) which is connected to the Xfinity Cable Gateway XB7 Modem/Router.

Resolution

I completed two tasks that ultimately fixed the issue, however I do not which one was the primary culprit or if it was both. 

First, I turned off IPv6 on my Arris W30.

Second, the Xfinity XB7 gateway wireless password was the same as my Arris W30.  Even though I don’t use the XB7 wireless capabilities, I changed the password so it was different. 

Opened up the Sonos App and presto, I was able to log in.  This was true across all iOS devices. 

I have no clue of the ins/outs of networking, and I am sure there others may chime in with the details, but I wanted to share just in case this helps a couple other people.