Traditionally, RSS Readers are programs run on your computer and thus require no login.
The only variants are popular, because you get the same experience from every device to sync subscribed feeds, read/unread counts etc.
You could host such a service yourself with something like tinytinyrss for example[0].
But you can just as well use any feed reader available for your platform of choice. Thunderbird for example has provided this feature for ages besides email.
They do of course also exist as terminal applications. One example would be newsboat[1].