Specifically I was writing that clients could get their cookies, but not served form the nginx cache. This has always been about whether or not the cached page was serving the cookies or not.

With the exact same configuration for the cache, there is a difference between:

location /

and

location /~home.html

in regards to whether or not the cached version of the page has the Set-Cookie headers in it.

I will try and research some more to see if that would be expected or not.