How to add / remove tabs from user profile?
If you don't want to use a contrib module like TabTamer then, In Drupal 7,   you can use hook_menu_alter to disable the MENU TAB by using access callback


    /**
     * Implementing hook_menu_alter
     * Restrict MENU TABS access
     */
    function MODULE_NAME_menu_alter(&$items) {
        if(/* check your conditions */) {
            $items['user/%user/hybridauth']['access callback'] = FALSE;//Change the MENU PATH as per your requirement.
        }
    }


Note


Get the MENU PATH by printing $items variable.