It does make a difference, actually.
The actual problem was that in our environment the size of the headers sent back by Discourse for the request going to /auth/yahoo are very large - 3897 bytes.
BUT when navigating around before trying to login, the headers (one of which is the cookie that has some pre-login session state) gets larger, e.g. up to a size of 4142 bytes. This is larger than the buffer which nginx allocates for holding that first part of the response.
Upping the size of proxy_buffer_size to 8k was necessary for our infrastructure and has solved the problem on try.discourse.org.
@Neil_Brooks2, please let me know (in a PM) which sites are yours and I will ensure those are deployed next, we can continue testing there and then we’ll roll out the change to everyone.