Aspyr Media today rolled out the Spring Update for Sid Meier's Civilization VI [Steam] for Linux gamers, but sadly cross-platform multiplayer still isn't ready. They did previously confirm to me directly that it would be in, but it's just not ready.
From their post on Steam:
QuoteUPDATE 4/20/17 - We are finally live with the Spring update!
Important note about cross platform multiplayer: While it was our sincere goal to have cross-platform play between Windows and Mac/Linux in this update, we were unable to meet that goal due to some immersion-breaking bugs that occur specifically with cross-platform play. Quality is simply too important to Aspyr and our partners so we elected to release this update while we continue to work on these remaining issues. Linux and Mac can still play with each other.
You can find the full release notes for the Spring Update on Steam here. It includes a lot of balances changes, AI tuning, bug fixes and plenty more.