@Jeruba Your answer clarifies the definitions beautifully.
I would support the censorship of communications whose clear purpose is to promote hatred and/or violence against an identifiable group. I would also censor depictions of sexual abuse of minors, e.g. child pornography and websites promoting the sexual exploitation of children or those below the age of consent (or those incapable of giving consent).
Explicit sexual materials should be restricted so that minors will not be exposed to them on broadcast media. In the home, parents or guardians have the right to block or lock out channels they believe are unsuitable for any (or all) family members.
The FTC and in Canada CRTC set and enforce broadcast standards to protect the public from exposure to whatever they deem unsuitable for general audiences.
That would include such things as (neo-)Nazi propaganda and those whose communication denies facts such as the Holocaust or the various well-documented genocides such as but but exclusive to the one in Rwanda.
I may choose to disregard or refuse to expose myself to communications that I consider offensive or misleading. Whether that is America’s Funniest Home Videos, the broadcasts of televangelists, or Barney the Dinosaur is up to me.