Hide specific post types created using the Pods framework from searches and archives if membership is required to access.

hide_my_pods_item_filter_post_types.php

<?php
/**
 * Hide the 'my_pods_item' post type from searches and archives if membership is required to access.
 * Update the $post_types[] array with one or more pod names you need to protect.
 *
 * You can add this recipe to your site by creating a custom plugin
 * or using the Code Snippets plugin available for free in the WordPress repository.
 * Read this companion article for step-by-step directions on either method.
 * https://www.paidmembershipspro.com/create-a-plugin-for-pmpro-customizations/
 */
function hide_my_pods_item_filter_post_types( $post_types ) {
    $post_types[] = 'my_pods_item';
    return $post_types;
}
add_filter( 'pmpro_search_filter_post_types', 'hide_my_pods_item_filter_post_types' );