The permissions over the App_Data folder might not be read, write, modify (full) and this prevents the css files from being read. Please make sure that you have these permissions. When in IIS the "network service" that is the user that connects to the site`s database or another user you might be using does not have full permissions over App_Data I think the anonymous user may get this problem.
By default Sitefinity 5.x uses Claims authentication, which might be the possible reasons for the exception
Missing configuration for the requesting relying party,
if the authentication has not been configured properly. Can you please try switching back to Forms authentication, following the instructions on this KB article
and let us know if any issues persist?
the Telerik team
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