WordPress. Why does the taxonomy post filter only show posts for the first taxonomy?

Question

PHP

Created custom_post_type (programs) and taxonomy (genretax). Now I want to display records on the archive-programs.php page depending on the taxonomy specified for them.
The layout uses the MixItUp 3 library (for the tile filter) https://www.kunkalabs.com/mixitup/ Now it looks like this:

And the problem is actually this:
if I specify several taxonomy names for one post (for example, scenic flights and heliskiing ) and for another post I will also indicate scenic flights and heliskiing in the taxonomies, then when filtering (when to choose heliskiing) there are no posts. That is, when each post is given a different taxonomy name, then everything is correct, and if they are the same, then it displays the first post .. For example,

1. Post "HELI-SKI WEEK IN WISTLER" -> taxonomy "Scenic flights";
2. Post "7 Days of Adventure in Hawaii" -> "Scenic Flights" taxonomy and "Private Tour" taxonomy ;
In this case, when clicking on the taxonomy "Scenic flights" will display posts 1 and 2, and when clicking on the taxonomy "Private tour" will not display anything.
Taxonomy output code:

<ul class="programs_list dark_icon_programs">
<?php $terms = get_terms('genretax');
    foreach($terms as $term){ ?>
    <li class="filter" data-filter=".category<?php echo $term->term_id; ?>"><?php echo $term->name; ?></li>
    <?php } ?>
</ul>

Custom post type output code:

<ul class="list_right_col_item_programs img_width">

<?php 
        $args = array(
          'post_type' => 'programs',
        );
        $query = new WP_Query( $args );

        if ($query->have_posts()) {

          while ( $query->have_posts() ) : $query->the_post(); ?>

              <li class="mix category<?php $terms = get_the_terms( $post->ID, 'genretax' );
                  if( $terms ){
                    $term = array_shift( $terms );
                    echo $term->term_id;
                  } ?>">
                    <a href="<?php the_permalink(); ?>" class="img_col_item_programs">
                        <?php echo get_the_post_thumbnail(get_the_ID()); ?>
                    </a>
                      <a href="<?php the_permalink(); ?>" class="link_col_item_programs"><?php the_title(); ?></a>
              </li>
            <?php endwhile;
        }
            wp_reset_postdata(); ?>
            </ul>

Please help, I can't figure it out..

Answer 1

Most likely, if the post has several categories, then they all need to be displayed in the tag<li>

$classes = array();
$classes[] = 'mix';

if ( $terms = get_the_terms( get_the_ID(), 'genretax' ) ) {
  foreach ( $terms as $key => $term ) {
    $classes[] = 'category' . $term->term_id;
  }
}

echo '<li class="' . implode( ' ', $classes ) . '">';