Rewrite query string for exposed taxonomy filter
You can accomplish this look by using Contextual Filters instead of an exposed filter in Views. But this approach will involve several changes. In a nutshell you would need to:


The list of tags on top would need to be a different (taxonomy) Views, embedded in the Header area of your catalogus View using Global: View area. In the taxonomy view, you will need to rewrite the output of the Taxonomy field (use "Rewrite results" in the taxonomy field) to a link that points to /catalogus/[field_portfolio_tags]
Add a Contextual Filter to your catalogus View. Be sure to add the taxonomy field Portfolio tags to the list of fields in this View (you can hide it if you don't want it to display for every single product). Choose the taxonomy Content: Portfolio tags. Choose Display all results in When filter value is not in URL. In WHEN THE FILTER VALUE IS IN THE URL OR A DEFAULT IS PROVIDED  choose Specify validation criteria. Validator: taxonomy term. Filter value type: term name converted to Term Id.


When you click on a taxonomy term in the embedded header View you will be redirected to /catalogus/name_of_tag. The Contextual Filter will assure that only products with that tag will be shown.

This should be it!