FCC doesn't regulate cable stations. Local municipalities do have contracts with cable companies for enforcing community standards. Would be funny if blue cities just started forcing Faux News to be dropped as a matter of preventing dissemination of harmful lies and distortions.
As much as I dislike Faux News (I dislike CNN too, and I lean left), I feel like silencing "fake news" is a slippery slope because for one reason or another, the US population doesn't understand what "facts" are, so red cities would probably just drop CNN on the pretense of it being "fake news," and then everyone just gets forced into their little bubbles and everyone loses.