I ended up finding some rogue code in my child theme’s function.php file. I think I had added this a while back to force the login/logout links to appear:

/*
add_filter('wp_nav_menu_items', 'add_login_logout_link', 10, 2); function add_login_logout_link($items, $args) {         ob_start();         wp_loginout('index.php');         $loginoutlink = ob_get_contents();         ob_end_clean();         $items .= '<li>'. $loginoutlink .'</li>';     return $items; }
*/

Removing this seems to have cleared up the issue for me.