There might be others but the main reason that the game kicks you from a room (or other players from a room you've created) is that it found that some of your files had been modified. The game doesn't verify all files but at least the ones in /data/scripts and data/gui (not sure about others).
Your game files might be modified due to different reasons, mostly by using mods or e.g. corrupted installation.

Files in subscribed (from Steam workshop) mods override games files. If the game detects that important (from multiplayer point of view) files are overriden then it you won't join any room except ones that use the same mod (usually marked with green/red gear - not sure what red one means).
To disable mod usually you can just:

• start Mod Manager from Steam/Library/Cossacks 3
  
• unselect / delete mods

or
modify/delete Steam\steamapps\common\Cossacks 3\mods\mods.ini (your mods subscription configuration) directly
or
go to Steam\steamapps\workshop\content\333420 (Cossacks 3 mods folder) and delete its content.

This way is even safer since after C3 reinstallation these mods get re-enabled by default w/o user realizing it.

Sometimes game files are just corrupted due to broken installation or just you changed them in e.g. text editor.
The easiest way to reset them is to use veryfing game files via Steam.
You can find it in Steam/Library/Cossacks 3/Right Mouse Button/Properties/Local files/Verify integrity of game files