I don't think that's possible. I think streaming in practice (not in theory!) is nowadays monitoring everything you do with the content they provide. In fact you yourself blocked your own TV from accessing the Internet.

Anyway I saw quite a few technical solutions (general purpose computers) but I didn't see any service to then use those with. There are quite a few streaming services I would trust though, e.g. public services like Arte.TV or PBS (well... I did, not I'd be cautious) that can be accessed without an account.

So it depends in the end of what kind of content you mean to stream. You don't have to answer that specifically but... if it's not something that is genuinely public, available on services like PeerTube but instead rely on surveillance capitalism, e.g. YouTube, Netflix, etc then I'd argue the kind of streaming itself you want is not compatible with your privacy requirements.

Edit: I'm not streaming except public radio (specifically fip.fr that's all) on my desktop. I just download the content I need what from whatever sources provide it DRM-free. It's both a technical alternative and a healthier practice IMHO.