The .config file is usually sitting in the same folder as the application, under Program Files. Everything under Program Files is ReadOnly, including your .config file, to normal users. Administrators on the machine don't have that restriction, so long as the code is running with the elevated permissions ("run as Administrator").
It is a BAD IDEA to open up permissions under Program Files so users can write to the config file. You can put your additional "all users on the machine" settings for you app in it's own configuration file in a folder under C:\ProgramData and/or "user-specific" settings in it's own configuration file in the users profile folder. Exactly which folders are appropriate depend on the situation the users are expected to use the app.
Check out Environment.SpecialFolder Enum (System) | Microsoft Docs
] for the folder locations you can get the paths for and what they are normally used for, and Environment.GetFolderPath Method (System) | Microsoft Docs
] for how to resolve those values to folder paths.
By the way, ConfigurationSettings is now obsolete having been replaced by ConfigurationManager