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I tried to play multiplayer with a friend. He has steam and i have the gog version.
We were able to join each others games using the codes, but when we started the game, it disconnected the second player. No crash, just disconnect.
Is this related to using different clients?
Having the same problem here, tried restarting the game and all types of lobbies and maps and it disconnected me (the one GOG user out of 4 of us) every time. The furthest in I got was playing the first turn before I got DC'd.
Have you checked that you had the same version ?

Have you tried to run it without Gog galaxy on your side and Steam on his ?
We had the same version.
After the new patch it worked, but if that was the fix i do not know.
I think it was/is related to his router settings. Last time we were at his place with both PCs.
This time, i was at my place and when he hosted we had the same error. It is really strange, because joining the lobby was possible. But it crashed after launching the game.
When i hosted it worked perfectly fine.