Don't fire tags for logged in Wordpress users

You could try a similar apporach to this: How to track form submissions using tag manager?

  1. Check for the existence of the admin bar with a customJS
function checkWpAdminBar() {
  var isWpAdmin = document.querySelector('#wpadminbar');
  
  if (isWpAdmin && isWpAdmin.style.display === 'block') { # ← check if it is set to block or delete the second check if the div is not present for non logged in users
    return true;
  } else {
    return false;
  }
}
  1. Make other tags dependent on this variable. (Don't execute this tag when any of these triggers have been triggered.)