Users who play on a bigger maps have requested for possibility to disable notifications for remote barbarians camps.
This is now implemented and could be enabled by editing the script file. Code will check if new camp is close enough to player's cities and only in this case notification will be shown.
User could manually set preferred minimum range following this instructions:

Navigate to folder 1316047367.
Open file BarbariansNotificationScript.lua (use Notepad).
First line should read:
local CITY_RANGE = 0;
Set it to any range you prefer for notifications to show.
Save, Close. Make sure it is still lua (not txt).