You need to add a filter in the /wp-includes/default-filters.php
Find this section:
// REST API filters.
add_action( 'xmlrpc_rsd_apis', 'rest_output_rsd' );
add_action( 'wp_head', 'rest_output_link_wp_head', 10, 0 );
add_action( 'template_redirect', 'rest_output_link_header', 11, 0 );
add_action( 'auth_cookie_malformed', 'rest_cookie_collect_status' );
add_action( 'auth_cookie_expired', 'rest_cookie_collect_status' );
add_action( 'auth_cookie_bad_username', 'rest_cookie_collect_status' );
add_action( 'auth_cookie_bad_hash', 'rest_cookie_collect_status' );
add_action( 'auth_cookie_valid', 'rest_cookie_collect_status' );
add_filter( 'rest_authentication_errors', 'rest_cookie_check_errors', 100 );
Then add a new filter like so:
add_filter( 'rest_authentication_errors', function( $result ) {
if ( ! empty( $result ) ) {
return $result;
}
if ( ! is_user_logged_in() ) {
return new WP_Error( 'rest_not_logged_in', 'You are not currently logged in.', array( 'status' => 401 ) );
}
return $result;
});
This solution is mentioned on the WordPress developer resources site, but they do not specifically tell you where to add the filter.
After this change, you should see this message when an un-authenticated user attempts to connect to the REST API:
{"code":"rest_not_logged_in","message":"You are not currently logged in.","data":{"status":401}}