Stardew Valley multiplayer could be finished as early as next month, according to a recent tweet from creator Eric Barone.
Update on Stardew Valley multiplayer: still making good progress on fixing bugs, if all goes well it should be ready in about a monthApril 10, 2018
In February, publisher Chucklefish said the multiplayer update has entered QA testing. "Work on the new features is done, and we’ve sent all the new text off to be translated into the different languages," Barone said at the time, adding that a public beta should be available for spring, which is consistent with today's update.
In the meantime, you can play modded multiplayer right now. It just takes a little elbow grease.