Trying to remove a couple categories from shop page

To alter products on shop page, you need to hook into woocommerce_product_query action:

/**
 * Exclude products from a particular category on the shop page
 */
function custom_pre_get_posts_query( $q ) {

    $tax_query = (array) $q->get( 'tax_query' );

    $tax_query[] = array(
       'taxonomy' => 'product_cat',
       'field' => 'slug',
       'terms' => array( 'clothing' ), // Don't display products in the clothing category on the shop page.
       'operator' => 'NOT IN'
    );


    $q->set( 'tax_query', $tax_query );

}
add_action( 'woocommerce_product_query', 'custom_pre_get_posts_query' );