Firefox is being updated by another instance

You can't change the option to check for updates while one is in progress. I'd suggest shutting the app down and then fully closing anything leftover in Task Manager.

Do you always run Firefox Portable via FirefoxPortable.exe? If not, it could be running in local mode like via associations of links or HTML files. If not, you can also remove those local folders if you're not using a local Firefox.

You'll need to start Firefox up and select "Check for updates but let you choose to install them" at this point.

If you want them entirely disabled, you can use a distribution policy. Create a folder called distribution within FirefoxPortable\App\Firefox64 (leave off the 64 if you're running on Windows 32-bit). Create a file called policies.json and add the following to it:

{
"policies": 
  {
    "DisableAppUpdate": true
   }
}

This entirely disables updates other than when you update it via the PA.c Platform or manually by downloading a new PA.c Format installer.