Call custom posttype outside the functions.php

Step-by-step:

If you put everything in your functions.php or plugin file, it should work just fine.

1. We need a user meta field, where User can decide if they want to activate a certain CPT.

   add_action( 'show_user_profile', 'my_user_meta_show_faq' );
   add_action( 'edit_user_profile', 'my_user_meta_show_faq' );
   add_action( 'user_new_form', 'my_user_meta_show_faq' );
   
   function my_user_meta_show_faq( $user ) {
       $show_faq = get_user_meta($user->ID, 'show_faq', true); ?>
       <h3>Show FAQs?</h3>
       <?php _e('Yes', 'my_textdomain');?>
       <input type="radio" name="show_faq" value="yes" <?php checked('yes', $show_faq); ?> /><br />
       <?php _e('No', 'my_textdomain');?>
       <input type="radio" name="show_faq" value="no" <?php checked('no', $show_faq); ?> /><br />
   <?php }
   
   add_action( 'personal_options_update', 'my_user_meta_save' );
   add_action( 'edit_user_profile_update', 'my_user_meta_save' );
   
   function my_user_meta_save( $user_id ) {
       if ( !current_user_can( 'edit_user', $user_id ) )
           return;
       if($_POST['show_faq'] === 'yes') {
           update_user_meta($user_id, 'show_faq', 'yes');
       } else {
           delete_user_meta($user_id, 'show_faq');
       }
   }
   

2. We need to query that option on WP init. If that option is true we register our CPT.

   add_action( 'init', 'my_cpt_init' );
   
   function my_cpt_init() {
       if ( !is_user_logged_in() )
           return;
       $current_user = wp_get_current_user();
       $show_faq = get_user_meta($current_user->ID, 'show_faq', true);
       if($show_faq === 'yes') {
           register_post_type( 'faq', array(
               'labels' => array(
                   'name' => __( 'Faq' ),
                   'singular_name' => __( 'Faq' )
               ),
               'public' => true,
               'has_archive' => true,
               'rewrite' => array('slug' => 'faq'),
               'publicly_queryable' => true,
               'supports' => array(
                   'title',
                   'editor'
               )
           ));
       }
   }
   

Now we can toggle the CPT with our state of the user meta field.