get_categories doesn’t allow you to set rand as orderby AFAIR, but that’s not a big deal. It returns an array, so in your case all you have to do is to shuffle that array:
<?php
$categories = get_categories( array(
'orderby' => 'name',
'order' => 'ASC',
'exclude' => 'all',
'include' => '135,19,124,133,126',
) );
shuffle ( $categories );
foreach ($categories as $category) {
echo '<div class="category-list">';
echo '<a href="' . get_category_link( $category->term_id ) . ' "><div class="image_wrapper2 is-image list-image">'. do_shortcode(sprintf('[wp_custom_image_category term_id="%s"]',$category->term_id)). '</div></a>' ;
echo '<div class="image-category-mosje"><h2 class="title-category"><a href=" ' . get_category_link( $category->term_id ) . ' "> '.$category->name.' </a></h2></div>';
echo '<span class="category-count"> ' . $category->count . '</span>';
echo '</div>';
}
?>