Problem: Browser displays "403 forbidden" in SharePoint with Forms authentication.
Context: Trying to get extended site to display the right page for forms authentications.
Cause: IIS (7.0) thought that the anonymous user did not have access to the web site, so it was not redirecting (or displaying) the internal page (the custom page with form authentication) for login.
Composite problem: Trying to enable anonymous access to 'the entire web site' was hidden in Advanced Permissions. That's because the Default Zone in Central Admin for the NTLM site (the base site of the extended Forms one) did not have Anonymous enabled.
Solution: I went to the Default zone in Central Admin, enabled anonymous (temporarily) for the base web site). Then I was able to enable anonymous access to the entire web site in Advanced Permissions (in the base site).
(For the record: anonymous authentication in IIS for the extended site had the identity of the app pool and not IUSR (win server 2008) and also ASP.NET impersonation enabled)