Thanks for the source code hint, I was looking at the rendered page. Looking at the source code hint, it appears that the complaint is about the script section at the very end. Which makes sense, it expects an XML document and instead receives an html document with a script at the end. The RSS reader can't interpret that, so to get any meaningful idea what is going on takes a fair bit. I think it might make more sense if, in response to a feed request, the api generated a "feed" that states the error?
Regarding the login requirement, I am not trying to get the feed to bypass it. TinyRSS can provide a login account and password, it just isn't working. I am trying to find out more about that.