You mean, when you set:

SOGoTrustProxyAuthentication = NO
SOGoEnablePublicAccess = YES

it works?

Yes.
I have another system with this traditional setting and it works there.
I tried it just now (for all cases ;-)

Fix pushed: https://github.com/inverse-inc/sogo/commit/1734b387a353cab21b1f768791af8983e9f9ec98

Test it buddy!

I used current git tree of both sogo and sope and I installed them on my testing machine now.
I use: sogod SOGoTrustProxyAuthentication YES

but sogo gives me it's own "Login page" as I would not use proxy-side authentication. 2.0.5 works correctly in this aspect with the same configuration.
So I cannot test Public Access now...

Instead of:

• (NSString ) checkCredentialsInContext: (WOContext ) context
  {
  NSString *remoteUser;

  if ([[SOGoSystemDefaults sharedSystemDefaults] trustProxyAuthentication])
  {
  remoteUser = @"anonymous";
  }
  else
  {
  / If such a header is not provided by the proxy, SOPE will attempt to
  deduce it from the "Authorization" header. /
  remoteUser = [[context request] headerForKey: @"x-webobjects-remote-user"];
  }

  return remoteUser;
  }

in SOGoProxyAuthentication.m, try:

• (NSString ) checkCredentialsInContext: (WOContext ) context
  {
  NSString *remoteUser;

  / If such a header is not provided by the proxy, SOPE will attempt to
  deduce it from the "Authorization" header. /
  remoteUser = [[context request] headerForKey: @"x-webobjects-remote-user"];

  if ([remoteUser length] == 0 && [[SOGoSystemDefaults sharedSystemDefaults] trustProxyAuthentication])
  {
  remoteUser = @"anonymous";
  }

  return remoteUser;
  }

Yes, now work them both - proxy-side authentication and Public Access.

Thank you Sir.

Updated patch: https://github.com/inverse-inc/sogo/commit/c08263d1c3d6444616f51643c409a4e2d7c02593