Dear Gregor,
After your site debuging we found problem in CRED frontend translation plugin. We will fix it in next version.
As temporary solution for you:
Make the custom fields translate in WPML translation management in Multilingual content setup or disable CRED frontend translation. Both these options will allow the shortcodes to be rendered in the frontend.
Please let me know if you are satisfied with my answer and if I can help you with any other questions you might have.
Regards,
Gen.