Fixing this is pretty easy. Just add a new authorization rule to your root web.config site that grants access to the stylesheet and/or other file resources that you want to allow anonymous access to.  For example, the below configuration section denies access to all resources except stylesheet.css:

Listing 2

<system.web>
   <authorization>
       <denyusers="?"/>
   </authorization>
</system.web>
<location path="stylsheet.css">
    <system.web>
       <authorization>
           <allow users="*"/>
       </authorization>
    </system.web>
</location>

Alternatively, if you have a directory with a lot of static files in it, you can just add a web.config file at its root and add a global authorization rule like above allowing access to it. 

Hope this helps,

Scott