I was able to get the snippet partial working by changing the code to the following:
<!-- Layout -->
<head>
{% include 'stylesheets' %}
</head>
<!-- Partial: _stylesheets.liquid -->
{{ stylesheets.file_url | stylesheet_tag }}
This iterates through each stylesheet, but I cannot for the life of me find out why it does so without a liquid for loop.
Any ideas why this works?