tl;dr: You can have Nginx with Shibboleth. Rebuild Shibboleth with FastCGI support, and recompile Nginx with a custom module: https://github.com/nginx-shib/nginx-http-shibboleth. You can now run the Shibboleth FastCGI authorizer and responder applications and successfully authenticate!
Full information on how to include the ngnix-http-shibboleth custom module with Nginx are provided on GitHub. This repository now serves as the canonical place for all documentation in this space.