Theming multi-value fields in Views
The only work-around solution that I can think of would be to:

Create a separate view for the tags.

Then there I will be able to uncheck display all values in same row.

Re-write field to &lt;div class="{{ field_tags }}"&gt; {{ field_tags }} &lt;/div&gt;

Then use View Fields View to insert the Tags view as a field in my other view and pass the nid as contextual filter. 

Probably not the best solution, so if anyone has a better one I'd love to hear it.