I had this problem with both Beta and full game: Neither Voice nor Text chat was working at all. No one could hear me, and i could not hear anyone else. Also text chat did not work (Error message "sorry, you're not allowed to chat...").
If you look into the FAQ you see that you have to allow SoT to access your Microphone (Windows 10 Privacy Settings)
The Mic privacy settings in Windows is just one part of the Problem, however.
You also have to enable Chat Access in your Xbox App Privacy settings (through Windows Live.com website).
Open your Xbox App
open your own profile
click on the "More" button and select "Privacy"
A web browser opens and you have to login to live.com using your Xbox account.
Under "others can..." check the setting on "Voice, Text or Invites" and change it from Block to Everyone (or friends if you are friends with all your teammates)
Confirm your changes.
Restart SoT and now you can both use text and voice chat.