I just performed a clean install of EE onto a local virtual host, and having checked the installation by successfully logging into the CP, followed that up by bringing into play the MasterConfig files. I copied those over from my last project since I had them modified from the basic FocusLab files (lots of config-variables added in, extra commented headers for my own reference, etc). I had used these same files to switch another project over to MasterConfig system just a few days ago, with no problem.
So I updated the system folder location in my webroot index.php and admin.php files, as normal, made sure all the folders were in the correct locations, and checked that all was okay by going to log into the CP. And got the response 'Unable to load the following extension file: ext.republic_variables.php'. Now, the project that these MasterConfig files were grabbed from did use Republic Variables. And since this is a virgin install, of course those extension files are not present. But since the only change between the successful CP login and the failed one was the introduction of the MasterConfig files (and some folder moving), I have to conclude that somewhere in the MasterConfig files there must be a reference to Republic Variables. But I absolutely cannot find it anywhere. Does anyone have any ideas what code in MasterConfig might be causing this?