Is it possible to uninstall XCode, keep the CLI tools and run a Homebrew on Mojave?

Yes.

I did it some time ago, so I do not remember exactly how I uninstalled Xcode. If there is no uninstall option in the App Store, I just move Xcode to the trash and delete it.

I was able to install the command line tools by:

  1. go to https://developer.apple.com
  2. to log in
  3. go to Account> Downloads> See more downloads

and there is an item called Command Line Tools (macOS 10.14) for XCode 10.2