We run into following problem:

•      We have application, that makes authenticated calls to sharepoint 2013 REST services (PUT and GET). Everything works well, when anonymous access
  

is turned off.

•      But we need to enable anonymous access for two or three lists. When this is done, request for FormDigest from C# code fails always with 403 result – forbidden.
  

•      I attach following code that is used for making the call. Again, it works fine when Anonymous Access is disabled for this site collection.
  
            var contextContent = new StringContent(string.Empty,Encoding.UTF8,"text/xml");
            var contextInfoRequest = await contextInfoClient.PostAsync(url + "/_api/contextinfo", contextContent);
            var contextInfoRequestStr = await contextInfoRequest.Content.ReadAsStringAsync();
  
            var formDigestXml = XDocument.Parse(contextInfoRequestStr);
            var formDigestNode = formDigestXml.Descendants(d + "FormDigestValue").First();
            var formDigest = formDigestNode.Value;
  
            var itemPostBody =
                Encoding.UTF8.GetBytes("{'__metadata':{'type':'" + entityTypeName + "'}, " + jsonProperties + "}");
  
            var addRequest = (HttpWebRequest)WebRequest.Create(queryUrl);
            addRequest.Method = "POST";
            addRequest.ContentType = "application/json;odata=verbose";
            addRequest.Accept = " application/atom+xml"; 
            addRequest.Headers["X-RequestDigest"] = formDigest;
  
            addRequest.Credentials = new NetworkCredential(user, pass, domain);
  
            var itemRequestStream = await addRequest.GetRequestStreamAsync();
            itemRequestStream.Write(itemPostBody, 0, itemPostBody.Length);
  

// Following line causes 403 Frobidden Exception:

            var itemResponse = (HttpWebResponse) await addRequest.GetResponseAsync();
            var respStream = itemResponse.GetResponseStream();
            var l = new List<byte>();
            while (respStream.CanRead)
            {
                var i = respStream.ReadByte();
                if (i == -1) break;
                l.Add((byte)i);
            }
            var xml = Encoding.UTF8.GetString(l.ToArray(),0,l.Count);