How to make sure content doesn’t display if selection is empty

The issue is that when you don’t have any speakers, you don’t have anything to pass to your include parameter.

You could solve it by wrapping the code in a conditional so it only runs if there are speakers attached to that post.

$speakers = get_post_meta( $post->ID, 'min_webinar_speaker', false );

if ($speakers != '') { // <- you may need to do a more thorough check than this
    ... run the code...
}