I had been getting the problem on my event submission page after recent updates.
After testing deactivation of other plugins and a revert to the default theme the event submission page would not display the date picker under any of the conditions.
I implemented the advise at https://msyk.es/blog/prevent-jquery-wordpress-theme/ making sure that I was loading jquery correctly and had wp_head and wp_footer placed in my theme.
I load Jquery this way in header.php.
<?php
add_action( 'wp_enqueue_script', 'load_jquery' );
function load_jquery() {
wp_enqueue_script( 'jquery' );
}
?>
I installed the “Use Google Libraries” plugin and the problem was resolved.
Hope that helps.