Thanks for the recent update it works. Now for better security I do not use username to login but only email address with custom login error message. When I applied the code below in my functions.php. The login error that shows is (invalid request) instead of (Invalid email or password) as indicated in the code below, also the limit login attempts does not work with the code below. Is there another way to achieve login with email address only without any form of compromise with the bp branded login plugin.

 remove_filter('authenticate', 'wp_authenticate_username_password', 20);

 
add_filter('authenticate', function($user, $email, $password){

    //Check for empty fields
    if(empty($email) || empty ($password)){        
        //create new error object and add errors to it.
        $error = new WP_Error();

        if(empty($email)){ //No email
            $error->add('empty_username', __('Email field is empty.'));
        }
        else if(!filter_var($email, FILTER_VALIDATE_EMAIL)){ //Invalid Email
            $error->add('invalid_username', __('Invalid email or password.'));
        }

        if(empty($password)){ //No password
            $error->add('empty_password', __('Password field is empty.'));
        }

        return $error;
    }

    //Check if user exists in WordPress database
    $user = get_user_by('email', $email);

    //bad email
    if(!$user){
        $error = new WP_Error();
        $error->add('invalid', __('Invalid email or password.'));
        return $error;
    }
    else{ //check password
        if(!wp_check_password($password, $user->user_pass, $user->ID)){ //bad password
            $error = new WP_Error();
            $error->add('invalid', __('Invalid email or password.'));
            return $error;
        }else{
            return $user; //passed
        }
    }
}, 20, 3);
 

Thanks for your support

I was also wondering if you can enable support for either of this 2 plugins to display limit login attempts counter on the bp branded login page for security reasons.

https://wordpress.org/plugins/limit-login-attempts-reloaded/
or
https://wordpress.org/plugins/limit-attempts/

similar problem was indicated here https://stackoverflow.com/questions/31066775/how-to-retrieve-wp-error-in-custom-login-form

I was able to edit the login.php template in my child theme but I still don’t know how to enable the remember me to be checked by default

Thanks