> there is no First Amendment right for RT to be carried on US cable networks.

There might be, but it would be the cable network's first amendment right to carry them, not RT's right to be carried.

The argument in court was kind of backwards, nobody violated TikTok's rights by taking them off the app store, but you could fairly easily argue that Apple and Google's rights were violated by telling them that they can't carry it. That would, presumably, require either Apple or Google to bring a lawsuit though, and they seem to want to play nice with the incoming administration.