Think I figured it out. Rather than put it in the actual page template, it goes in the functions.php:
// Function to randomize Advanced Custome Fields' Repeaters
function my_acf_load_value3( $value, $post_id, $field )
{
shuffle($value);
return $value;
}
// Randomize ACF Clients' Repeater
add_filter('acf/load_value/name=clients', 'my_acf_load_value3', 10, 3);