What precedent are you using to imagine that if Facebook/Youtube/etc were to become public utilities, that they would be barred from censorship? Public broadcasters are currently regulated by the FEC:
https://www.fcc.gov/media/radio/public-and-broadcasting#OBSC...
> Indecent Material. Indecent material is protected by the First Amendment, so its broadcast cannot constitutionally be prohibited at all times. However, the courts have upheld Congress' prohibition of the broadcast of indecent material during times of the day when there is a reasonable risk that children may be in the audience, which the Commission has determined to be between the hours of 6 a.m. and 10 p.m. Indecent programming is defined as “language or material that, in context, depicts or describes, in terms patently offensive as measured by contemporary community standards for the broadcast medium, sexual or excretory organs or activities.” Broadcasts that fall within this definition and are aired between 6 a.m. and 10 p.m. may be subject to enforcement action by the FCC.