It’s very good that you are using Advanced Custom Fields.
Use this for assigning running dates to movie and by making use of WP_Query you can call movies wherever is matching date.
For fetching posts you can use following code:
$args = array(
'post_type' => 'movie',
'meta_key' => 'date',
'meta_query' => array(
array(
'key' => 'date',
'value' => array('2016-10-08'),
'compare' => '=',
),
),
);
$query = new WP_Query( $args );