How to enable 3rd party cookies ONLY for Microsoft Teams
Add a cookie exception for https://login.microsoftonline.com. This worked for me at least.
After login you can check in Chrome what cookies it uses.
Third party would be: .skype.com and maybe .online.lync.com
If you use IE you might have *.microsoft.com in your Trusted Zone but .skype.com is not and IE/Edge will throw error. (as sites are in different zones)
At the bottom left (click on the guid error code d928....) of your screenshot you can download a log file (to check details what URL are called and what the issue is)
I added all 4 entries and teams.microsoft.com is now working in Chrome with 3rd party cookies disabled. Thanks for the posts.
Where to add
chrome://settings/content/cookies under Allow
What I added
[*.]microsoft.com
[*.]microsoftonline.com
[*.]skype.com
[*.]online.lync.com