If you create a new profile and host one of the existing campaigns, without mods, does that work properly if people join (also from a new profile)?
If so, try a new basic campaign without mods (with just the minimum done that someone can test joining), and then with the same mods.
If you have problems with one of the existing campaigns, tried switching who is hosting, and see if that makes a difference, or helps narrow the problem down to specific system(s).
If you start a second instance of the game, do you have any problems when joining by LAN?
Start the game, switch to windowed mode and lower the game resolution (and maybe check the option to mute the sound volume when the game doesn't have focus), start the GM campaign, hit Esc, open the Connectivity Menu, optionally disable online multiplayer (if it is enabled) and make sure LAN Connections is enabled (or that can be done in the options before starting a new game).
Next, start the game again from the '..\SteamApps\common\Divinity Original Sin 2\DefEd\bin\EoCApp.exe' program file (doesn't matter if the first instance is started through Steam/Galaxy or the executable), select Play Campaign in the Game Master section, switch to the LAN tab, rather than Online, and join. That should work, since both instances of the game are using the same data, and only the local networking is involved.
Try having everyone verify local files: in the Steam library, right click on the game and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Files...' button.
With the GOG version, in the (optional) Galaxy client, select the game, then the settings icon at the top right (beside the Play button) and under Manage Installation select 'Verify / Repair'.