Magento – Magento newsletter unsubscribe link not working

You need to rewrite Magento's Customer Mage_Customer_Block_Account_Navigation Block class.

create config.xml file in the app/code/local/Neo/CustomerNavigationLinks/etc

<?xml version="1.0"?>
<config>
    <modules>
        <Neo_CustomerNavigationLinks>
            <version>0.0.1</version>
        </Neo_CustomerNavigationLinks>
    </modules>
    <global>
        <blocks>
            <customer>
                <rewrite>
                    <account_navigation>Neo_CustomerNavigationLinks_Block_Account_Navigation</account_navigation>
                </rewrite>
            </customer>
        </blocks>
        <helpers>
            <customernavigationlinks>
                <class>Neo_CustomerNavigationLinks_Helper</class>
            </customernavigationlinks>
        </helpers>
    </global>
</config>

in Neo/CustomerNavigationLinks/Block/Account/ careate a file called Navigation.php with the following content in it

<?php

class Neo_CustomerNavigationLinks_Block_Account_Navigation extends Mage_Customer_Block_Account_Navigation
{
    public function removeLinkByName($name)
    {
        unset($this->_links[$name]);
        return $this;
    }
}
?>

in app/etc/modules create a file called Neo_CustomerNavigationLinks.xml with the following content

<?xml version="1.0"?>
<config>
    <modules>
        <Neo_CustomerNavigationLinks>
            <active>true</active>
            <codePool>local</codePool>
        </Neo_CustomerNavigationLinks>
    </modules>
</config>

Now in local.xml add following content

<customer_account>
        <reference name="customer_account_navigation">
            <action method="removeLinkByName">
                <name>newsletter</name> 
            </action>
        </reference>
</customer_account>

Try {{var subscriber.customer_firstname}}

Take a look at

/app/code/core/Mage/Newsletter/Model/Queue.php

/**
 * Send messages to subscribers for this queue
 *
 * @param   int     $count
 * @param   array   $additionalVariables
 * @return Mage_Newsletter_Model_Queue
 */
public function sendPerSubscriber($count=20, array $additionalVariables=array())
{
    ....

    $collection = $this->getSubscribersCollection()
        ->useOnlyUnsent()
        ->showCustomerInfo()
        ->setPageSize($count)
        ->setCurPage(1)
        ->load();

    ....

    foreach($collection->getItems() as $item) {
        $email = $item->getSubscriberEmail();
        $name = $item->getSubscriberFullName();

        $sender->emulateDesign($item->getStoreId());
        $successSend = $sender->send($email, $name, array('subscriber' => $item));

Then take a look at /app/code/core/Mage/Newsletter/Model/Resource/Subscriber/Collection.php