All posts are still shown when adding category argument to query

First: don’t use query_post for secondary loops. It alter the main query and you can end up with wire results. Instead use a new WP_Query instance. See this question for detail info.

Now with your proble. You are using the “cat” parameter and that is for “category” taxonomy, not for your custom taxonomy. You should use the tax_query parameter instead:

<?php
$tax_query =  array(
                 'taxonomy' => 'team_categories',
                 'field'    => 'slug',
                 'terms'    => 'noukogu'
              );

$args = array(
    'post_type' => 'team',
    'tax_query' => array( $tax_query ),
 );

$query = new WP_Query( $args );

if ( $query->have_posts() ) {
    while ( $query->have_posts() ) {
        $query->the_post();

        $title = str_ireplace( '"', '', trim(get_the_title())); $desc=str_ireplace( '"', '', trim(get_the_content()));
        ?>

        <div class="member">
          <img class="image" src="https://wordpress.stackexchange.com/questions/159034/<?php print team_thumbnail_url($post->ID) ?>" alt="liikme pilt">
           <h3 class="title"><?php echo $title; ?></h3>
            <p class="description">
                <?php echo $desc; ?>
            </p>

      </div>
      <!-- End member -->

   <?php
   }
}

wp_reset_postdata();
?>

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