If you want customer grid reindex programmatically, you can use the below step.

1. Create file menu.xml on app/code/Magemonkeys/CustomerReindex/etc/adminhtml

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Backend:etc/menu.xsd">
    <menu>
        <add id="Magemonkeys_CustomerReindex::customer_reindex" title="Eagle Rocket" translate="title" module="Magemonkeys_CustomerReindex"
             sortOrder="50" resource="Magemonkeys_CustomerReindex::manage_customer_reindex" parent="Magento_Customer::customer"/>
        <add id="Magemonkeys_CustomerReindex::customer_manage" title="Customer Reindex" translate="title" module="Magemonkeys_CustomerReindex"
             sortOrder="10" parent="Magemonkeys_CustomerReindex::customer_reindex" action="customerreindex/customerindexer/index" resource="Magemonkeys_CustomerReindex::manage_customer_reindex"/>      
    </menu>
</config>

2. Create file routes.xml on app/code/Magemonkeys/CustomerReindex/etc/adminhtml

<?xml version="1.0"?>

<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:App/etc/routes.xsd">
    <router id="admin">
        <route id="customerreindex" frontName="customerreindex">
            <module name="Magemonkeys_CustomerReindex" before="Magento_Backend" />
        </route>
    </router>
</config>

3. Create file Index.php on app/code/Magemonkeys/CustomerReindex/Controller/Adminhtml/Customerindexer

<?php
namespace MagemonkeysCustomerReindexControllerAdminhtmlCustomerindexer;
class Index extends MagentoBackendAppAction
{
    protected $indexFactory;
    protected $indexCollection;
    protected $resultRedirectFactory;

    public function __construct(
        MagentoBackendAppActionContext $context,
        MagentoIndexerModelIndexerFactory $indexFactory,
        MagentoIndexerModelIndexerCollectionFactory $indexCollection,
        MagentoFrameworkControllerResultRedirectFactory $resultRedirectFactory,
        MagentoFrameworkMessageManagerInterface $messageManager 
    )
    {
        parent::__construct($context);
        $this->indexFactory = $indexFactory;
        $this->indexCollection = $indexCollection;
        $this->resultRedirectFactory = $resultRedirectFactory;
        $this->_messageManager = $messageManager;
    }

    public function execute()
    {
        $indexerCollection = $this->indexCollection->create();
        $indexids = $indexerCollection->getAllIds();

        $indexid = 'customer_grid';
        $indexidarray = $this->indexFactory->create()->load($indexid);
        $indexidarray->reindexAll($indexid);

        $resultPage = $this->resultRedirectFactory->create();        
        $resultPage->setPath('customer/index/index');
        $this->_messageManager->addSuccess(__("Customer Reindex Successfully."));
        return $resultPage;            
    }    
}

4. Output