//functions.php
function search_distinct() {
    return "DISTINCT";
}
add_filter('posts_distinct', 'search_distinct');

//archive.php
<?php
    $args = array(
       'post_type' => 'homily',
       'posts_per_page' => -1,
       'meta_key' => 'homilist',
       'orderby' => 'meta_value',
       'order' => 'ASC'
    );
    $the_query = new WP_Query( $args );

    search_distinct(); //Correct?

    if ( $the_query->have_posts() ) {
       echo '<ul>';
           while ( $the_query->have_posts() ) {
              $the_query->the_post();
                    echo '<li>' .the_field('homilist') . '</li>';
                }
        echo '</ul>';
     }
     wp_reset_postdata(); ?>