My friend and I both just bought the game (neither of us played the early access).
We successfully started a game together (over the internet, me hosting) and made it through the first 15 or so minutes just fine.
Shortly after reaching the deck of the ship we experienced a desyc, with my friend appearing to run off the side of the ship on my screen but walking around normally on his, unable to interact with anything.
Reloading earlier saves cause the issue to happen again, more or less immediately, before even reaching the deck this time. Sometimes his character runs off the edge, sometimes it stays still (presumably depending on if it was moving when the desync happened). He continues to be able to correctly observe the actions my character is taking even after his becomes screwy.
We have tried putting steam in offline mode and using the direct connection, but the problem still happens.