Does America allow the existence of any TV station propagating communism?

It might not have been allowed back in the mid 1950's when Senator Joe McCarthy was running rampant looking for communists. He did manage to blacklist some Hollywood people and others who incurred his wrath. He must have forgotten all about the 1st amendment and our freedom of speech. Ok...to answer your question, there wouldn't be any reason to stop a privately owned station from propagating communism. It's up to you as to whether you want to listen.