/*** The  filters ****/
    <?php $categories = get_terms('roller'); ?>
    <ul class="cat-list">
      <li><a class="cat-list_item active" href="#!" data-slug="">All projects</a></li>

      <?php foreach($categories as $category) : ?>
        <li>
          <a class="cat-list_item" href="#!" data-slug="<?= $category->slug; ?>" data-type="upphovspersoner">
            <?= $category->name; ?>
          </a>
        </li>
      <?php endforeach; ?>
    </ul>


 /****** The script*******/
<script>
$('.cat-list_item').on('click', function(e) {
    $('.cat-list_item').removeClass('active');
    $(this).addClass('active');

    $.ajax({
        type: 'POST',
        url: '/wp-admin/admin-ajax.php',
        dataType: 'html',
        data: {
          action: 'filter_projects',
          taxonomy: $(this).data('slug'),
        },
        success: function(res) {
          $('.project-tiles').html(res);
        }
    })
});
</script>

<?PHP
/******* functoins.php *******/
function filter_projects() {
    $postType = $_POST['type'];
    $catSlug = $_POST['taxonomy'];

    $projects = new WP_Query([
       'post_type' => 'upphovspersoner',
       'posts_per_page' => -1,
       'tax_query' => [
          [
             'taxonomy' => 'roller',
             'field'    => 'slug',
             'operator' => 'IN'
          ],
       ]
    ]);
    $response = '';

    if($ajaxposts->have_posts()) {
      while($ajaxposts->have_posts()) : $ajaxposts->the_post();
        $response .= include('framework/upphovspersoner-item.php');
      endwhile;
    } else {
      $response = 'empty';
    }

    echo $response;
    exit;
  }
  add_action('wp_ajax_filter_projects', 'filter_projects');
  add_action('wp_ajax_nopriv_filter_projects', 'filter_projects');
?>