I believe you are thinking of common carrier status Eirikrautha. That doesn’t really have anything to do with websites. At any rate what you are talking about is simply forcing websites to publish content. They aren’t required to give everyone a platform but you are free to go and host your own content. That isn’t censorship.
”Not many people know I owned the first radio in Springfield. Weren’t much on the air then. Just Edison reciting the alphabet over and over. “A,” he’d say. Then “B.” “C” would usually follow."