I end up having a remote proxy to serve the wiki however when I successfully log in, when I got redirect, I got a denied action page and not being logged anymore.
I tried to debug the DokuWiki code to find my issue myself, currently I only found out that the REMOTE_USER variable seems to not exist anymore when redirected.
I thought this variable was set in result of an Authorization header which isn't sent with the non-working method (trought the reverse proxy) and working (direct) one.
I tried to use the cookie from a successful login (from a direct connection) to the non working case but it keep denied it.
So overall how the default login (with ACL plugin) works in order to look for what I miss in the reverse proxy configuration.
When I looked at the fiddler log I didn't see any significant difference.
I tried to override, in doku.php in the header, some server variables (like HTTP_HOST, SERVER_PORT, SERVER_NAME, REMOTE_ADDR) to set back the original value like if they were no proxy. Didn't change anything.