AT LAST! Great news, with macOS 14.4 and above, Apple now provides an official way to disable the orange dot on external screens (projectors, etc), without disabling SIPS or other hacks:
Copy pasting the instructions here for posterity:
Turn off privacy indicators for external displays on your Mac
Requires macOS Sonoma 14.4 or later
To hide privacy indicators β the orange and green dots that appear next to Control Centre in the menu bar to show that your microphone or camera is in use β on an external display while viewing an app in full screen, first execute a system override command in Terminal. Then turn off privacy indicators for external displays in System Settings.
- Start up from macOS Recovery:
- Use macOS Recovery on a Mac with Apple silicon
- Use macOS Recovery on an Intel-based Mac
- From the Utilities menu in the menu bar, choose Terminal.
- Enter this command:
system-override suppress-sw-camera-indication-on-external-displays=on - Quit Terminal.
- From the Apple menu, choose Restart.
- After your Mac has restarted, choose Apple menu ο£Ώ > System Settings, then click Privacy & Security in the sidebar.
- Click Microphone (or Camera).
- Turn off Privacy Indicators for Microphone (or Camera) Access.