Using template_preprocess_field doesn't work, I assume, because this is a field from a View, not a node.
I've looked at this answer however that only seems to apply to the field value not the markup and styles surrounding it.
For example: The output of the field in markup is currently:
<div class="views-field views-field-field-status">
<div class="field-content">
Active
</div>
</div>
I'd like to conditionally add classes:
<div class="views-field views-field-field-status">
<div class="field-content my-conditionally-added-class">
Active
</div>
</div>