I'm on the Steam version, and there's a few things I did in combination that worked. First I changed the .exe in Program Files (x86)\Steam\steamapps\common\Sid Meier's Civilization IV Beyond the Sword\Beyond the Sword/Civ4BeyondSword.exe to run in Administrator mode. Spoiler : Then I went to the FFP Github and took the FinalFrontierGameUtils.py there, and used it to replace the one in my mod installation. I have it uploaded here in .xml (Civfanatic won't upload .py files), but it's supposed to be a .py file. Make sure to change the file extension back. Spoiler : Then what I did is create a desktop shortcut to boot up the mod directly. Make sure it's run as an Administrator, which happened for me automatically after I changed the .exe Spoiler : Put "mod= Mods/Final Frontier Plus" at the end in the Target line, without quotation marks, and make sure there's a space after the .exe" This altogether fixed my issues, though it's possible just replacing the .py file is enough.
It seems like the FinalFrontierGameUtils.py file gets corrupted in the installation somehow. I couldn't say why.