Just noticing this thread.
With respect to your original question about Git and Jenkin's CSRF setting, as you've surmised, Jenkins protects all POST requests when this feature is enabled. There's a snippet in the Subversion plugin wiki[1] about how to make Subversion's commit hook work with the CSRF protection, and I would expect the same pattern will work for Git.
With respect to authentication, CSRF is only tangentially related to authentication. If your Jenkins instance requires an authenticated login, the CSRF will factor that into the crumb. If your Jenkins allows anonymous access, the CSRF protection will use other information for the crumb.
-- Dean