WP_Query do not include posts with a certain value in a custom field –

Question

Try adding the type parameter:

$args = array('post__not_in' => $exclude,
    'ignore_sticky_posts' => 1,
    'posts_per_page' => 5,
    'meta_query'=> array(
        array(
        'key'=>'my_featured_post',
        'value'=> 1,
        'type' => 'numeric', // assuming your custom_value is an int, not a string.
        'compare'=>'!='
        )
    )
);
$query = new WP_Query($args);