You can only disable voice/video calling on the browser version of the Facebook Messenger, you can't disable it on the Facebook Messenger App.
So, if you want to prevent someone from calling or chatting with you, you should follow these steps:
- Click the gear icon at the bottom of the chat sidebar.
- Go to Advanced Settings
- Enter friends' names or a friend list in the box .
- Click Save. You will no longer appear as available on chat to these friends and automatically call will be blocked.
