There are a lot of unhappy users in this thread on the Xfinity forums:
https://forums.xfinity.com/conversations/xfinity-stream-website/xfinity-streaming-service-requires-login-everytime-i-use-it-apple-tv/63ccba40d9aa6753d37a826f
I'm hoping that complaining about it here might catch the attention of some Xfinity devs who can help fix it.
I've found Comcast/Xfinity has all kinds of odd telemetry end points going on (assuming some is ads, some is for in-product observability) that gets blocked on many DNS blocklists and causes all kinds of weird glitches when using their services.
Might be something to double-check.
(Edit: I’m talking about the AppleTV hardware device, and my iCloud account.)
My favorite thing I saw is that they score you as a customer. If you call a lot they devalue you so when you go to quit they let you go rather than keep you
I’ve been having problems with the Prime Video AppleTV app having issues with taking a really long time to log in, throwing up some error messages before finally connecting.
And working for AWS I was able to find the correct chat room and talk directly to one of the developers. They had me try a few things and gave up.
And as another commenter here mentioned, my first thought was maybe some of my network filtering. But Prime Video works fine on my computers, phone, and console.