You want to prevent emails being sent for all new messages?
Try this in your theme/functions.php or in plugins/bp-custom.php
remove_action( 'messages_message_sent', 'messages_notification_new_message', 10 );
If that doesn’t work, try writing a function using this hook:
do_action_ref_array( 'messages_message_sent', array( &$message ) );
Found in: bp-messages\bp-messages-functions.php
In that function, remove all the recipients from $message.
Thanks, @shanebp! Not sure how to mark this as [Resolved]