Do you know if it is possible to use Nginx with Shibboleth?
Not until FastCGI supports "authorizer" mode. The Shibboleth 2 documentation describes a FastCGI SP application but explains that it doesn't work with Nginx because it lacks the "authorizer" mode needed for the filter.
Poster Alex on this Rails thread shares Ruby code for Shibboleth auth but appears to have used Apache. Other posters using Nginx still couldn't make it work.