Hi @atjesse – currently the only way to accomplish this is via the rest_{$this->post_type}_query filter. You can add a custom tax_query object using this filter. See: https://core.trac.wordpress.org/browser/tags/4.7.1/src/wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php?marks=258#L246

Can you create a Trac ticket for this enhancement? Here is a guide for doing that: https://make.wordpress.org/core/handbook/tutorials/trac/opening-a-ticket/

Here is a similar ticket that is closely related, please take a look and link back to it from your ticket: https://core.trac.wordpress.org/ticket/39494