Magento 2 – How to Add External JS

I would advise using Require JS to load this rather than adding it via XML like this, but if you're adamant you want to do it this way try this:

<!-- Bugherd -->
<referenceBlock name="head.additional">
    <block class="Magento\Framework\View\Element\Text" name="my_script">
        <action method="setText">
            <argument translate="true" name="text" xsi:type="string">
                <![CDATA[
                    <script type='text/javascript'>
                    (function (d, t) {
                      var bh = d.createElement(t), s = d.getElementsByTagName(t)[0];
                      bh.type = 'text/javascript';
                      bh.src = 'https://www.bugherd.com/sidebarv2.js?apikey=dkjfsd89id6sftsdghkjn3';
                      s.parentNode.insertBefore(bh, s);
                      })(document, 'script');
                    </script>
                ]]>
             </argument>
        </action>
     </block>
</referenceBlock>

Same as mtr.web's answer but uses class rather than block.

This error looks to be specific to require.js, in particular:

an anonymous module that ends up having the same name as one of the named modules in the script loaded by the manually coded script tag.

In your case, I believe you may be trying to load an anonymous define() module somewhere else in your code that has the same name as a module in the loaded dropin.min.js script tag (define(). The require.js docs recommend the following:

• Be sure to load all scripts that call define() via the RequireJS API. Do not manually code script tags in HTML to load scripts that have define() calls in them.
• If you manually code an HTML script tag, be sure it only includes named modules, and that an anonymous module that will have the same name as one of the modules in that file is not loaded.
• If the problem is the use of loader plugins or anonymous modules but the RequireJS optimizer is not used for file bundling, use the RequireJS optimizer.
• If the problem is the var define lint approach, use /*global define */ (no space before "global") comment style instead.

Do you encounter the same error when trying to load the un-minified version of the Drop-In?