A note for those who have just bought the game and are trying to play multiplayer, but can't because of the issue seen in the screenshot (Many thanks to Falran from GOG support for giving me the solution):

Reverting the game to the previous update (Version 1.143 logo) allowed me to enter the serial and join a multiplayer game.

To revert updates, use the menu button to the right of the play button in GOG Galaxy and click Manage installation-> Configure -> Installation -> Uncheck "Automatically update to newest version". Then pick "Version 1.143 logo". (FYI: I currently don't know how to get an older version without using GOG's client)

For some reason though, updating it back to the newest patch still produces the same bug even after the key has been entered, so it needs to be left on the older version.

This should not affect anything unless playing the Russian version, however, as according to patch notes I found on the GOG forum the only thing that changed, ironically, was "fixed an issue with the multiplayer keys not working correctly in the Russian version of Mount & Blade: With Fire & Sword".

Wow!! It actually works :) After a long time, that I purchased this title, finally I can play multiplayer...
GOG should make available all the patches for download... or at least the logo version installer also for download...
Additionally a clear description on how to make your game work should be made available by gog... :(

Because multiplayer never worked for me, about one year or so, until now :)) I had reserves in purchasing other titles, with multiplayer component included. I even considered contacting consumer rights agencies :))

So... is the fix version, russian version ? :/

Thx for this :) I might add you to my friends list :) if... you... :)