My friends and I have never had this problem before playing beta.  Two of us are playing against 6 computers on Hyperion's Gate.  We played for about 50 minutes when we realized that a system that I was full of militia in my end was taken by one of the AI on my friend's end (Diplominator).

I'll detail all the strangeness (probably too detailed) as best I can from each of our perspectives.  I will be "W" and my friend will be "D."

W - Allied with Purple and Yellow is focused on attacking D
D - W does not have allies. Yellow is focused on attacking D

W - Planet adjacent to the star is full of militia and uncolonized. I run my 11 ships out of the system and lose 1
D - Planet is taken by Purple and Purple's fleet is attacking W's fleet of 12 ships and gets out with all of them

W - Yellow has been holding a planet all game. D was fighting for the whole game
D - D took the planet about 10 minutes before we realized the desync

W/D - ships were completely different across the whole map.  All the buildings matched except on the planets that were taken by different players from each of our POV's. We didn't think to look at those ones (seems like an easy thing to remember lol)

Witayifier held the same planets on both versions which made us think that the games were not desynced (I rename when I play against AI so we could tell that much).  Diplominator's planets were 2 or 3 different.  We got way too confused to see all the other differences.

Trying to host the saved game crashes both our computers and we get a minidump.

We need some sort of way to tell that we aren't playing the same game.  There were never messages that we switched to being controlled by AI (that's our best guess at what happened).  We only noticed one spot of lag, but that was too late in the game for the desync to have happened.  Also, Diplominator could still pause my game so our games were still connected.